Name: VII OFICINA NACIONAL DE TEORIA QUÂNTICA DE CAMPOS //////////////////// VII NATIONAL WORKSHOP ON QUANTUM FIELD THEORY
Start: 2021-12-08T00:50:00-03:00
End: 2021-12-10T19:30:00-03:00
Location: Virtual Meeting, Universidade Federal da Bahia, Brazil

VII OFICINA NACIONAL DE TEORIA QUÂNTICA DE CAMPOS //////////////////// VII NATIONAL WORKSHOP ON QUANTUM FIELD THEORY

from Wednesday 8 December 2021 (00:50) to Friday 10 December 2021 (19:30)

Monday 6 December 2021
Tuesday 7 December 2021
Wednesday 8 December 2021

09:15

09:15 - 09:30
09:30 Non-linear causality in Israel-Stewart like fluid theories - Fábio Sperotto Bemfica (Universidade Federal do Rio Grande do Norte)
Non-linear causality in Israel-Stewart like fluid theories
- Fábio Sperotto Bemfica (Universidade Federal do Rio Grande do Norte)
09:30 - 10:05
Israel-Stewart like theories (IS) describe relativistic viscous fluids that obey first order partial differential equations in its variables, being appealing theories from a numerical-modeling point of view. Furthermore, the IS theory is one of a few theories that has been proven to be causal and stable after small perturbations around equilibrium, both in the linear regime. After the detection of the quark-gluon plasma (QGP) in the 2000's (whose formation occurs in ultra-relativistic heavy-ion collisions resulting in a liquid behavior of the quarks, anti-quarks, and gluons that move independently in such high energy conditions), IS like theories have been widely used with great success to describe this kind of plasma. However, when dealing with a relativistic theory, nonlinear causality is essential, especially within far from equilibrium situations like the QGP. In this talk, I will present a recent result where, for the first time, sufficient conditions have been obtained for nonlinear causality and local well-posedness of IS like theories. Also, necessary conditions are obtained, imposing some strong constraint over the transport coefficients of the theory. In particular, these necessary conditions have been used in recent works to show that several results obtained so far for the QGP are based on numerical simulations that violate causality.
10:05 Intervalo
Intervalo
10:05 - 10:10
10:10 Color-kinematics duality, double copy and the unitarity method for higher-derivative theories - Gabriel Menezes
Color-kinematics duality, double copy and the unitarity method for higher-derivative theories
- Gabriel Menezes
10:10 - 10:45
In this talk we will discuss color-kinematics duality for higher-derivative Yang-Mills amplitudes. We will show how such amplitudes can be used to construct quadratic-gravity amplitudes from the double copy method. We will also illustrate the use of the generalized unitarity method for loop amplitudes containing resonances with a brief discussion on two specific one-loop examples.
10:45 Intervalo
Intervalo
10:45 - 11:10
11:10 Brane inflation models - Francisco Brito (UFCG)
Brane inflation models
- Francisco Brito (UFCG)
11:10 - 11:45
In this talk I will revisit recent studies of brane inflation models and their viability with respect to observational data.
11:45 Almoço
Almoço
11:45 - 14:00
14:00 A quantum field theory approach to critical dynamics: the role of multiplicative noise - Daniel Barci
A quantum field theory approach to critical dynamics: the role of multiplicative noise
- Daniel Barci
14:00 - 14:35
Quantum Field Theory has proven to be a very powerful tool for describing continuous phase transitions. The spontaneous symmetry breaking paradigm, complemented with the Renormalization Group (RG), allows us to classify phase transitions into ``universality classes"\footnote{J. L. Cardy, {\it Scaling and renormalization in statistical physics}, Cambridge lecture notes in physics (1996).}. In this way, it is possible to determine different correlation functions and the associated observables in the neighborhood of a critical point. However, the dynamics of a phase transition, when the system is taken out of thermodynamic equilibrium, is still an open research problem. This problem is placed in a much wider context, which is the theoretical formulation of out-of-equilibrium statistical mechanics. The interest in critical dynamics is rapidly growing up in part due to the wide range of multidisciplinary applications in which criticality is a central issue. For instance, the collective dynamics of biological systems presents critical behavior displaying space-time correlation functions with non-trivial scaling laws\footnote{A. Cavagna, {\it et.\ al.\ }, Phys. Rev. Lett. {\bf 123}, 268001 (2019).}. Other interesting examples come from epidemic spreading models where dynamic percolation is observed near multicritical points\footnote{H. K. Janssen, M. Muller, and O. Stenull, Phys. Rev. {\bf E70}, 026114 (2004)}. Moreover, strongly correlated systems, such as antiferromagnets in transition-metal oxides present a very rich phase diagram including ordered as well as topological phases. These compounds are generally described by quantum field theory models~\footnote{B. Hsu and E. Fradkin, Phys. Rev. B {\bf 87}, 085102 (2013).} (Quantum Lifshitz and related Sine Gordon models) that seem to have anomalous critical dynamics. The usual approach to critical dynamics is the ``Dynamical Renormalization Group (DRG)", early described in a seminal paper by Hohenberg and Halperin\footnote{P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. {\bf 49,} 435 (1977).}. The simplest starting point is to admit that, very near a critical point, the dynamics of the order parameter is governed by a dissipative process driven by an overdamped additive noise Langevin equation. The critical point is approached by integrating out short distance (high momentum) degrees of freedom in order to obtain the dynamics of an equivalent effective long distance (small momentum) model. As usual in RG theory, the integration over higher momentum modes generates all kind of couplings, compatible with the symmetry of the problem. For this reason a consistent study of a RG flux should begin, at least formally, with the most general Hamiltonian containing all couplings compatible with symmetry. Interestingly, in a similar way, DRG transformations generate couplings that modify the probability distribution of the original stochastic process. In particular, we will show that one loop perturbative corrections generates couplings compatible with a multiplicative noise stochastic processes, even in the case of assuming an additive processes as a starting point. In this presentation, we show how to deal with the dynamics of an order parameter near criticality, assuming a dissipative process driven by a general multiplicative noise Langevin equation. We will analyze a simple model of a not conserved real scalar order parameter, $\phi({\bf x},t)$ with quartic coupling $\phi^4({\bf x},t)$. We assume, as a starting point, a multiplicative noise Langevin equation, modeled by a general dissipation function $G(\phi)=G(-\phi)$, with the same symmetry of the Hamiltonian, $Z_2$. To compute dynamical correlation functions, we use a generalized Martin-Siggia-Rose-Janssen-DeDominicis formalism (MSRJD) that represents the Langevin dynamics by a quantum field theory. We use a recently developed approach to deal with multiplicative noise in a general stochastic prescription\footnote{Z. G. Arenas and D. G. Barci, Phys. Rev. {\bf E85}, 041122 (2012); Journal of Statistical Mechanics: Theory and Experiment {\bf 2012}, P12005 (2012); M. V. Moreno, Z. G. Arenas and D. G. Barci, Phys. Rev. {\bf E91}, 042103 (2015).}. In this formalism, the generating functional is written in terms of a functional integral over four fields, two bosonic and two fermionic that, in certain conditions, display Supersymmetry. As it is well known, the upper critical dimension of this model is $d_c=4$. For $d>4$, the Gaussian fixed point with dynamical critical exponent $z=2$ is stable. For, $d< 4$, the Gaussian fixed point becomes unstable and the Wilson-Fisher fixed point shows up in a first order expansion around $\epsilon=4-d$. In this case, the dynamics is governed by $z=2+O(\epsilon^2)$, and all multiplicative noise coupling constants are irrelevant. In this sense, we recover very well known old results. However, the dynamic dramatically changes at $d=2$. Here, all multiplicative noise couplings are marginally relevant, flowing to a novel stable fixed point dominated by a multiplicative noise stochastic process\footnote{Nathan Silvano and Daniel G. Barci, {\it Critical Dynamics: multiplicative noise fixed point in 2D systems}, to be published, 2022}. The Brazilian agencies: FAPERJ, CNPq and CAPES-Finance Code 001, are acknowledged for partial financial support.
14:35 Intervalo
Intervalo
14:35 - 14:40
14:40 Quantum fluctuations, dispersive forces, some related effects and recent research - Danilo Teixeira Alves
Quantum fluctuations, dispersive forces, some related effects and recent research
- Danilo Teixeira Alves
14:40 - 15:15
We give an overview of quantum fluctuations and dispersive forces, briefly discussing, for example, the van der Waals, Casimir-Polder, Casimir, and dynamical Casimir forces. We make a brief discussion on some main articles on these phenomena, also presenting some contributions to the knowledge of these effects obtained by our research group in UFPA-Brazil. For instance: our prediction of the peak, valley, and intermediate regimes in the lateral van der Waals force; of a repulsive lateral van der Waals force; the possibility of generating motion of an object, induced by asymmetric excitation of the quantum vacuum; the existence of relativistic (non-parabolic) bands in the discrete spectrum of created particles in an oscillating cavity; the prediction of an enhancement of the dynamical Casimir effect by decreasing the mirror reflection.
15:15 Sessão 1
Sessão 1
15:15 - 16:40
Contributions

15:15 Critical Dynamics of Multiplicative Systems - Nathan de Oliveira Silvano (Rio de Janeiro State University - UERJ)

15:25 Newtonian and Carrollian limits of gravity theories in the first order formalism - Amanda Guerrieri Melchior (Centro Brasileiro de Pesquisas Físicas)

15:35 Considerations on the photon-photino mixing in presence of fermion condensates and space-time anisotropies - João Paulo da Silva Melo (Centro Brasileiro de Pesquisas Físicas (CBPF))

15:45 Master equations governing the coupling between spin-currents and gravity - Alexandre De Camargo (Universidade Federal Fluminense)

15:55 Feynman amplitudes in compact spaces up to all orders - Erich Cavalcanti (CBPF)

16:05 Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes - Daniel Martínez-Tibaduiza (Universidade Federal Fluminense)

16:15 Properties of Mesons in a Dense and Hot Medium - Elenilson Santos Nery

16:25 An effective field theory approach to the interactions of the doubly charmed state $T_{cc} ^+$ with a hadronic medium - Hildeson Paulo Lessa Vieira (Universidade Federal da Bahia)
16:40 Dynamical symmetry breaking from derivative four-fermion models - Tiago Mariz (Instituto de Física, UFAL)
Dynamical symmetry breaking from derivative four-fermion models
- Tiago Mariz (Instituto de Física, UFAL)
16:40 - 17:15
This work investigates the dynamical symmetry breaking from derivative four-fermion models by calculating the one-loop effective potentials. We demonstrate that they are positively defined and possess a continuous set of minima. We finally calculate the effective action of the corresponding models.
17:15 Intervalo
Intervalo
17:15 - 17:20
17:20 Towards to the Yang-Mills ensemble - Diego Fiorentini (universidade federal fluminense)
Towards to the Yang-Mills ensemble
- Diego Fiorentini (universidade federal fluminense)
17:20 - 17:55
We review our recent work on the new procedure to quantize the Yang-Mills theories in the continuum, which points towards the existence of a Yang-Mills ensemble. In the new approach, the idea is to divide the configuration space into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. To implement this mechanism, the gauge fields are mapped into an auxiliary field space used to initially determine sectors labeled by center vortices, and then separately fix the gauge on them. The whole procedure results into a BRST-invariant local action which turns out to be renormalizable to all orders. We provide examples of configurations belonging to sectors labeled by center vortices and we discuss the importance of the mapping injectivity, and show that this property holds infinitesimally for typical configurations of the vortex-free sector and for the simplest example in the one-vortex sector. Finally, we show that these configurations are free from Gribov copies.
Thursday 9 December 2021
09:30 Spontaneous chiral symmetry breaking in holographic QCD - Alfonso Ballon Bayona
Spontaneous chiral symmetry breaking in holographic QCD
- Alfonso Ballon Bayona
09:30 - 10:05
We describe the emergence of spontaneous chiral symmetry breaking in holographic QCD via a non-linear extension of the soft wall model with non-minimal couplings. We investigate the behaviour of meson masses and decay constants as a function of the quark mass. In the chiral limit we show the emergence of Nambu-Goldstone bosons in the pseudo-scalar sector and reproduce the Gell-Mann-Oakes-Renner (GOR) relation. Reference: 2107.10983 (accepted in Phys. Rev. D).
10:05 Intervalo
Intervalo
10:05 - 10:10
10:10 Effective field theories applied to studies of hadron physics - Kanchan Khemchandani
Effective field theories applied to studies of hadron physics
- Kanchan Khemchandani
10:10 - 10:45
I use effective field theories to study low energy interactions among hadrons and the consecutive formation of resonant/bound states in hadronic systems. The states formed in such systems are often referred to as dynamically generated or molecular states. In such studies, we consider the hadrons to be the degrees of freedom and the corresponding Lagrangians are constructed by requiring the symmetries appropriate and applicable to a given system. In this talk I will present the details and results of our recent works.
10:45 Intervalo
Intervalo
10:45 - 11:10
11:10 Qubitization of Quantum Field Theories - Paulo Bedaque
Qubitization of Quantum Field Theories
- Paulo Bedaque
11:10 - 11:45
Simulation of quantum field theories by quantum computers requires not only the discretization of spacetime but also of field space. Naive truncations of field space break symmetries and change the universality class of the theory, complicating the continuum limit. We discuss how one can have finite dimensional Hilbert spaces that “fit” into a quantum computer while, at the same time, reproducing the correct continuum physics. This is demonstrated in the solvable 1+1 dimensional O(3) sigma-model where the qubitization is accomplished using ideas of non-commutative geometry.
11:45 Almoço
Almoço
11:45 - 14:00
14:00 TFD formalism and applications in a gravitational theory - Alesandro Santos (UFMT)
TFD formalism and applications in a gravitational theory
- Alesandro Santos (UFMT)
14:00 - 14:35
The theory of Gravity is classical by its origin while other fundamental forces describing microscopic aspects of nature are quantum mechanical. There are several attempts to unify gravity with forces in the Standard Model. The search to unify gravitation and electromagnetism has a long history. The first studies were carried out by Faraday, Maxwell, Heaviside, Weyl, Kaluza-Klein, among others. A formal analogy between the gravitational and the electromagnetic fields led to the notion of Gravitoelectromagnetism (GEM) to describe gravitation. GEM allows scattering processes with gravitons as an intermediate state like the photon for electromagnetic scattering. The GEM has been extended from a theory of classical gravity to a quantized theory that allows a perturbative approach to calculating phenomena in gravity. In order to investigate the gravitational effects at finite temperature, the Thermofield Dynamics (TFD) formalism is considered. TFD is a real-time formalism of quantum field theory at finite temperature. There are two necessary basic ingredients to construct this formalism: (i) the doubling of degrees of freedom in a Hilbert space and (ii) the Bogoliubov transformations. So, after a brief introduction of these two theories, GEM and TFD, we will study some gravitational effects at zero and finite temperature. Furthermore, the analogy between gravity and electromagnetism will be explored in the context of the Lorentz-violating standard model extension.
14:35 Intervalo
Intervalo
14:35 - 14:40
14:40 Bumblebee fluctuations in curved spacetimes - Euclides Silva (Universidade Federal do Cariri)
Bumblebee fluctuations in curved spacetimes
- Euclides Silva (Universidade Federal do Cariri)
14:40 - 15:15
The bumblebee field is a self-interacting vector field whose vacuum expectation value (vev) defines a privileged direction in spacetime. This spontaneous breaking of the Lorentz symmetry has been extensively studied in flat spacetimes, wherein the bumblebee fluctuations give rise to two Nambu-Goldstone transverse mode and one longitudinal massive mode. In flat spacetimes, the NG transverse mode behaves like a gauge vector field. In this talk, we discuss the features of the bumblebee fluctuations in curved spacetimes. By assuming a $AdS_5$ five dimensional spacetime and a cosmological Friedmann-Robertson-Walker (FRW) 3-brane embedded, we found a exponentially suppressed self-interacting constant with respect to the extra dimension. For a spacelike vev along the extra dimension, we employed a Kaluza-Klein (KK) dimensional reduction for both models. The transverse mode diverges along the extra dimension and then, an extended bumblebee-dilaton theory is required to trap the massless KK mode on the brane in the noncompact extra dimension model. The conservation of the bumblebee current prevents the longitudinal mode to acquire a KK mass. Along the brane, the massless KK transverse mode behaves like a Maxwell field whereas the longitudinal mode is suppressed by the cosmological expansion.
15:15 Sessão 2
Sessão 2
15:15 - 16:40
Contributions

15:15 Linearity and Uniqueness in One Loop Fermionic Odd Amplitudes at Even Dimensions - José Fernando Thuorst (Centro Brasileiro de Pesquisas Físicas)

15:25 Geometrically constrained kinklike configurations - Matheus Lião

15:35 Effective field model for the description of the strong decays of the $B_c$ meson - João Vitor Cerqueira (UFBA)

15:45 Boundary Effects on Constituent Quark Masses in a four-fermion interaction model - Emerson Correa

15:55 Vertex $\nu$–$e^{-}$–$\phi^{+}$ of neutrino autoenergy in external magnetic field using the Ritus method - Natália Alvarenga

16:05 Topological BPS vortices in a Chern-Simons-CP(2) model in the presence of magnetic impurities - Marcos Vinícius C. Almeida (Universidade Federal do Maranhão)

16:15 BPS Maxwell Chern Simons vórtices with internal structures the abelian Higgs case - JOAO LUIS BRANDAO ANDRADE

16:25 BPS solitons in a Maxwell baby Skyrme model with a nontrival dielectric function - Eduardo da Hora
16:40 Pion observables in Minkowski space. - Wayne de Paula
Pion observables in Minkowski space.
- Wayne de Paula
16:40 - 17:15
We present a dynamical model for describing the pion structure. We based our analysis considering the pion as a bound state of a quark anti-quark pair interacting through a one-gluon exchange. Using the Nakanishi integral representation, we solve the Bethe-Salpeter equation directly in Minkowski space. We obtain the pion weak decay constant, the LF-momentum distributions, the valence probability, the distribution amplitudes, the probability densities and the electromagnetic form factor, with a good agreement with available experimental data.
17:15 Intervalo
Intervalo
17:15 - 17:20
17:20 QCD effective charges and the proton structure function at small-$x$ - Emerson Luna
QCD effective charges and the proton structure function at small-$x$
- Emerson Luna
17:20 - 17:55
In this talk we will briefly review the application of QCD effective charges, whose infrared behavior is constrained by a dynamical mass scale, in phenomenology. We illustrate the power of effective charges for studying the effect of higher twist operators of the Wilson operator product expansion in the proton structure function $F_{2}$ at small-$x$
Friday 10 December 2021
09:30 Towards hidden symmetries in gauge theories - Gabriel Luchini (Universidade Federal do Espírito Santo)
Towards hidden symmetries in gauge theories
- Gabriel Luchini (Universidade Federal do Espírito Santo)
09:30 - 10:05
The non-abelian generalization of the gauge symmetry proposed by C. N. Yang and R. Mills in 1954 was done à la Maxwell, i.e., in terms of a set of partial differential equations. However, the integral formulation counterpart of this generalization was not known until quite recently. The critical problem in constructing the integral Yang-Mills equations is the need for a consistent definition of the flux of the non-abelian electric and magnetic fields with which we can build a relationship with the dynamically conserved charges in such a way that these charges are invariant under gauge transformations. Indeed, the naive definition of the flux of the non-abelian fields $\Phi(F) = \int_{\Sigma}F_{\mu\nu}\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau}d\sigma d\tau$ is strongly dependent of the gauge choice since under a local gauge transformation $g(x)$, $F_{\mu\nu}(x) \to g(x)F_{\mu\nu}(x)g^{-1}(x)$ and therefore, the flux through a closed surface cannot be directly associated to gauge-invariant charges inside. The problem of finding the gauge-invariant charges in non-abelian gauge theories is therefore linked to the problem of formulating the integral version of the Yang-Mills equations. By scanning the $3+1$ dimensional Minkowski space-time with closed 2-dimensional surfaces based at a reference point $x_R$, which are in turn scanned by a family of homotopically equivalent loops based at $x_R$, it can be shown that the flux of the ``conjugate field-strength'' $F^W_{\mu\nu}(x) = W^{-1}F_{\mu\nu}(x)W$ through that closed surface, with $W$ being the holonomy defined along a loop from $x_R$ to $x$, will transform, under a local gauge transformation $g(x)$, as $\Phi \to g(x_R) \Phi g(x_R)^{-1}$, i.e., bringing the gauge group element to that defined at the reference point. A relation between the flux of the conjugate field through the closed surface $\partial \Omega$ and quantities evaluated inside the volume $\Omega$ can be established and expanding this construction for the dual field strength $\widetilde{F}_{\mu\nu}=\frac{1}{2}\epsilon_{\mu\nu\sigma\rho}F^{\sigma \rho}$, with the use of the (differential) Yang-Mills equations \begin{eqnarray} D_\mu F^{\mu\nu} &=& J^\nu_\textrm{e}\\ D_\mu \widetilde{F}^{\mu\nu} &=& J_\textrm{m}^\nu, \end{eqnarray} with $D_\mu \star = \partial_\mu \star + ie[A_\mu,\star]$ the covariant derivative, $F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu + ie[A_\mu,A_\nu]$ the field strength and $J^\mu_{\textrm{e},\textrm{m}}$ the electric and magnetic currents, we obtain their integral formulation: \begin{eqnarray} \oint_{\partial\Omega}W^{-1}F_{\mu\nu}W\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau}d\sigma d\tau = \int_{\Omega}\epsilon_{\lambda\mu\nu\gamma}W^{-1}J_\textrm{m}^{\gamma}W\frac{\partial x^{\lambda}}{\partial \zeta}\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau} d\sigma d\tau d\zeta \nonumber\\ +\int_{\Omega}\int_0^\sigma [F^W_{\mu\nu}(\sigma),F^W_{\alpha\beta}(\sigma^\prime)]\bigg(\frac{\partial x^\beta}{\partial \zeta}(\sigma^\prime)\frac{\partial x^\nu}{\partial \tau}(\sigma) - \frac{\partial x^\beta}{\partial \tau}(\sigma^\prime)\frac{\partial x^\nu}{\partial \zeta}(\sigma) \bigg)\frac{\partial x^\alpha}{\partial \sigma^\prime}\frac{\partial x^\mu}{\partial \sigma}d\sigma^\prime d\sigma d\tau d\zeta \end{eqnarray} \begin{eqnarray} \oint_{\partial\Omega}W^{-1}\tilde{F}_{\mu\nu}W\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau}d\sigma d\tau = \int_{\Omega}\epsilon_{\lambda\mu\nu\gamma}W^{-1}J_\textrm{e}^{\gamma}W\frac{\partial x^{\lambda}}{\partial \zeta}\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau} d\sigma d\tau d\zeta \nonumber\\ +\int_{\Omega}\int_0^\sigma [\tilde{F}^W_{\mu\nu}(\sigma),F^W_{\alpha\beta}(\sigma^\prime)]\bigg(\frac{\partial x^\beta}{\partial \zeta}(\sigma^\prime)\frac{\partial x^\nu}{\partial \tau}(\sigma) - \frac{\partial x^\beta}{\partial \tau}(\sigma^\prime)\frac{\partial x^\nu}{\partial \zeta}(\sigma) \bigg)\frac{\partial x^\alpha}{\partial \sigma^\prime}\frac{\partial x^\mu}{\partial \sigma}d\sigma^\prime d\sigma d\tau d\zeta. \end{eqnarray} In order to obtain the conserved charges, we consider the generalization of the holonomy operator by assigning to each loop parameterized by $\tau$, scanning a closed 2-dimensional surface with base-point at $x_R$, the quantity $ \mathcal{B}=\oint_\gamma W^{-1}B_{\mu\nu}W\frac{\partial x^{\mu}}{\partial \sigma}\frac{\partial x^{\nu}}{\partial \tau}d\sigma$ and define the 2-holonomy by the differential equation \begin{equation} \frac{dV}{d\tau}+ieV\mathcal{B} = 0, \end{equation} whose solution is the ordered series \begin{equation} V[\partial \Omega] = V_\circ\;P_2\;e^{-ie\oint W^{-1}B_{\mu\nu}W\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau}d\sigma d\tau}. \end{equation} This same operator can be obtained if we consider the 2-dimensional surface where it is calculated to be the result of continuous deformations from an infinitesimal surface at $x_R$. This leads to a definition of the 2-holonomy as the ordered series \begin{equation} V[\Omega] = P_3\;e^{ie\int_{0}^{2\pi}\mathcal{A}(\zeta)d\zeta}\;V_\circ \end{equation} with \begin{eqnarray*} \mathcal{A} &=& \int_\Sigma VW^{-1}\left(D_\lambda B_{\mu\nu}+D_\mu B_{\nu\lambda}+D_\nu B_{\lambda \mu}\right)WV^{-1}\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau}\frac{\partial x^\lambda}{\partial \zeta}d\sigma d\tau\\ &+&ie\int_\Sigma V \int_{0}^{\sigma}\left[\mathcal{F}_{\mu\nu}^W(\sigma'),B^W_{\mu\nu}(\sigma)\right]\left(\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^{\nu}}{\partial \zeta}\frac{\partial x^\alpha}{\partial \sigma'}\frac{\partial x^\beta}{\partial \tau} - \frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^{\nu}}{\partial \tau}\frac{\partial x^\alpha}{\partial \sigma'}\frac{\partial x^\beta}{\partial \zeta}\right)V^{-1}d\sigma d\tau \end{eqnarray*} where $\mathcal{F}_{\mu\nu} = F_{\mu\nu}-B_{\mu\nu}$. The fact that the operator $V$ can be calculated in these two different but equivalent approaches lead us to the identity \begin{equation} P_3\;e^{ie\int_{0}^{2\pi}\mathcal{A}(\zeta)d\zeta}= P_2\;e^{-ie\oint W^{-1}B_{\mu\nu}W\frac{\partial x^\mu}{\partial \sigma}\frac{\partial x^\nu}{\partial \tau}d\sigma d\tau}. \end{equation} For $B_{\mu\nu} = \alpha F_{\mu\nu} + \beta \widetilde{F}_{\mu\nu}$, the above equation, which is the non-abelian Stokes theorem, leads to the integral Yang-Mills equations. Two given closed surfaces in space-time can be regarded as points in the loop space $L^2\Omega$ and the volume between them will define a path in this space. A consequence of the integral Yang-Mills equations is that the operator $V[\Omega]$ is path-independent in $L^2\Omega$, i.e., it does not change under a reparameterization of the volume enclosed by $\partial \Omega$. By appropriately splitting space-time into space and time one can then show that $V$ evolves from a $t=0$ volume $\Omega_0$ to a $t>0$ volume $\Omega_t$ as \begin{equation} V[\Omega_t] = UV[\Omega_0]U^{-1}, \end{equation} i.e., it undergoes a unitary tranformation, thus preserving its eigenvalues which can be identified with the conserved charges. The integral Yang-Mills equations can be regarded as a zero-curvature equation in the loop space $L^2\Omega$ and the conserved charges are a consequence of the hidden gauge symmetry there.
10:05 intervalo
intervalo
10:05 - 10:10
10:10 Recent results on localized structures - Matheus Araújo Marques (Universidade Federal da Paraíba)
Recent results on localized structures
- Matheus Araújo Marques (Universidade Federal da Paraíba)
10:10 - 10:45
Localized structures usually appear in Field Theory under the action of scalar fields. In 2003, a new class of global defects was introduced by D. Bazeia, J. Menezes and R. Menezes in [Phys. Rev. Lett. 91, 241601 (2003)], where they presented a procedure to circumvent Derrick’s theorem in $(D,1)$ spacetime dimensions. This motivated us to use the scalar field to modify other localized structures. In this talk, we present some recent results in this direction. In particular, we consider the study of planar vortices in models with $U(1)\times Z_2$ symmetry, in which the magnetic permeability of the system is controlled by a neutral scalar field [D. Bazeia, M.A. Marques and R. Menezes, Phys. Lett. B 780, 485 (2018)]. In this case, using first order differential equations, the neutral scalar field decouples from the other ones, working as an independent structure, so it can be seen as a source for the vortex. In this sense, we show that it may modify the geometry of the vortex in a significant manner, generating an internal structure in its magnetic field, with ringlike configurations. Using a similar approach, and also considering a model with $U(1)\times U(1)$ symmetry, we can also get multilayered vortices, with several rings in the magnetic field [D. Bazeia, M.A. Liao, M.A. Marques and R. Menezes, Phys. Rev. Research 1, 033053 (2019)]. Other investigation to be presented in the talk concerns the inclusion of the neutral scalar field to control the dynamical terms in the Lagrangian density associated to magnetic monopoles, with $SU(2)\times Z_2$ models [D. Bazeia, M.A. Marques and R. Menezes, Phys. Rev. D 97, 105024 (2018)]. In this situation, using first order differential equations, we have found that not only the additional scalar field is capable of inducing an internal structure in the magnetic monopole, but also of modifying the behavior of its tail, leading to compact monopoles. These results also encouraged us to investigate novel configurations of monopole. In [D. Bazeia, M.A. Marques and Gonzalo J. Olmo, Phys. Rev. D 98, 025017 (2018)] we have found minimum energy solutions that leads to unusual monopole profiles, being small or hollow. In particular, the small monopole is described by analytical solutions. We also show some results of the work done in [D. Bazeia, M.A. Marques and R. Menezes, Phys. Rev. D 98, 065003 (2018)], in which we have replaced the additional $Z_2$ symmetry by a $SU(2)$ one, so the scalar fields was exchanged by a set of scalar and gauge fields. In this case, the additional fields are decoupled, so they can be understood as an independent monopole that interacts with the other one and modify it. Using small, hollow and the standard monopoles, we proposed composite structures, formed by a core and a shell or by two shells, which we have called bimagnetic monopoles. We also present the recent investigation in electrically charged structures, where the scalar field is used to control the electric permittivity of the medium in which a single charge is placed [D. Bazeia, M.A. Marques and R. Menezes, Eur. Phys. J. C 81, 94 (2021)].
10:45 Intervalo
Intervalo
10:45 - 11:10
11:10 Localized solutions of inhomogeneous nonlinear systems: dimensional reduction and similarity transformation - Wesley Cardoso (Universidade Federal de Goiás)
Localized solutions of inhomogeneous nonlinear systems: dimensional reduction and similarity transformation
- Wesley Cardoso (Universidade Federal de Goiás)
11:10 - 11:45
Solitary waves or solitons are a special type of solution that emerge due to a perfect balance between the nonlinear and dispersive/diffusive effects of the system. Depending on their form these solutions can be classified as bright, dark, breathers, rogue waves, etc. Various systems are described by the nonlinear Schrödinger (NLS) equation and its generalizations, and the interest includes nonlinear optics [1], Bose-Einstein condensates (BECs) [2], plasmas [3], hydrodynamics [4], photorefractive problems [5], nematic liquid crystals [6], and electrical line transmission [7]. In particular, new interesting solutions are possible when the NLS equation admits variable coefficients modulated in the spatial and/or temporal coordinates [8-13]. In the case of BECs, inhomogeneity can be easily controlled using Feshbach resonance [14]. Additionally, laser beams can be used to control the pattern of the confinement profile of the system. BECs can be tightly confined in one or two transverse directions by a strong potential, allowing us to study, respectively, the dynamics of quasi-two-dimensional or quasi-unidimensional of such a system. In this sense, one can apply some approximations to reduce the 3D NLS equation, alias Gross-Pitaevskii equation, to effective 1D [15-18] and 2D [19-21] equations. In particular, the use of the variational approximation for the transverse profile of the wave function, presented in [15, 16], helps to derive an effective 1D nonpolynomial Schrödinger equation, which accurately models the axial dynamics of the cigar-shaped BECs. This method can also be applied for the derivation of effective 2D- NPSEs, when BEC is strongly confined in the axial direction [15, 20]. In addition, by applying the standard adiabatic approximation and using an accurate analytical expression for the corresponding local chemical potential, the authors of Ref. [19] derived an effective 1D equation that governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. Next, in Ref. [17] was proposed a generalization of Ref. [19] for BECs trapped with anharmonic transverse potentials. In this presentation, we will briefly review the works on dimensional reduction and on the modulation of localized solutions obtained analytically through the similarity transformation technique. References [1] G.P. Kivshar and Y. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, New York, 2003) [2] S. Pitaevski and L.P. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003) [3] H.-H. Chen and C.-S. Liu, Phys. Rev. Lett. 37, 693 (1976) [4] A.R. Osborne, E. Segre, G. Boffetta, and L. Cavaleri, Phys. Rev. Lett. 67, 592 (1991) [5] W. Trillo and S. Torruellas (eds.), Spatial Solitons (Springer, Berlin, 2001) [6] G. Assanto (ed.), Nemations: Spatial Optical Solitons in Nematic Liquid Crystals (Wiley, New Jersey, 2013) [7] M. Remoissenen, Waves Called Solitons (Springer, Berlin, 1999) [8] A.T. Avelar, D. Bazeia, and W.B. Cardoso, Phys. Rev. E 79, 025602 (2009) [9] W.B. Cardoso, A.T. Avelar, and D. Bazeia, Nonlinear Anal.-Real World Appl. 11, 4269–4274 (2010) [10] A.T. Avelar, D. Bazeia, and W.B. Cardoso, Phys. Rev. E 82, 057601 (2010) [11] W.B. Cardoso, H.L.C. Couto, A.T. Avelar, and D. Bazeia, Commun. Nonlinear Sci. Numer. Simul. 48, 474 (2017) [12] W.B. Cardoso, J. Zeng, A.T. Avelar, D. Bazeia, and B.A. Malomed, Phys. Rev. E 88, 025201 (2013) [13] L. Calaça, A.T. Avelar, D. Bazeia, and W.B. Cardoso, Commun. Nonlinear Sci. Numer. Simul. 19, 2928–2934 (2014) [14] B.A. Malomed, Soliton Manegement in Periodic Systems (Springer, New York, 2006) [15] L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 65, 043614 (2002). [16] L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 66, 043603 (2002). [17] H.L.C. Couto, A.T. Avelar, and W.B. Cardoso, Ann. Phys. 530, 1700352 (2018). [18] M.C.P. dos Santos and W.B. Cardoso, Phys. Lett. A 383, 1435 (2019). [19] A. Muñoz Mateo and V. Delgado, Phys. Rev. A 77, 013617 (2008). [20] L. Salasnich and B.A. Malomed, Phys. Rev. A 79, 053620 (2009). [21] L. Salasnich, W.B. Cardoso, and B.A. Malomed, Phys. Rev. A 90, 033629 (2014).
11:45 Almoço
Almoço
11:45 - 14:00
14:00 Suppression of two-bounce windows and solitary oscillations in kink-antikink collisions - Fabiano de Carvalho Simas (Universidade Federal do Maranhão)
Suppression of two-bounce windows and solitary oscillations in kink-antikink collisions
- Fabiano de Carvalho Simas (Universidade Federal do Maranhão)
14:00 - 14:35
In this talk, I will address the kink-antikink collisions in (1,1)-dimensions. For this, we start to briefly review of the $\phi^4$ and $\phi^6$ models, as well as the standard mechanism of a resonant effect between the vibrational and translational modes. The role of extra vibrational modes in the scattering process will then be discussed, with particular emphasis on the total suppression of two-bounce windows, despite the presence of a vibrational mode, the production of multiple antikink-kink pairs and appearance of solitary oscillations.
14:35 Intervalo
Intervalo
14:35 - 14:40
14:40 Extended multi-scalar field theories in (1 + 1) dimensions - Alexis Roa Aguirre (UNIFEI-Brazil)
Extended multi-scalar field theories in (1 + 1) dimensions
- Alexis Roa Aguirre (UNIFEI-Brazil)
14:40 - 15:15
In this talk, I am going to present the explicit construction of some multi-scalar field theories in (1 + 1) dimensions supporting BPS solutions. The construction is based on the ideas of the so-called extension method. In particular, I am going to discuss some interesting field theories constructed from non-trivial couplings between several sine-Gordon fields.
15:15 Sessão 3
Sessão 3
15:15 - 16:40
Contributions

15:15 Dark Monopoles in Grand Unified Theories - Maria de Lourdes Deglmann

15:25 Bottom-charmed meson spectrum from a QCD approach based on the TDA - F. Miguel

15:35 Investigation of magnetized plasmas in Maxwell-Carroll-Field-Jackiw electrodynamics - Filipe Ribeiro

15:45 Effects of CPT-odd terms of dimensions three and five on electromagnetic propagation in continuous matter - Pedro D. S. Silva (UFMA)

15:55 Anderson localization induced by interaction - Mateus Calixto Pereira dos Santos (Universidade Federal de Goiás)

16:05 Magnetic monopoles in a nutshell - Philipe De Fabritiis (Centro Brasileiro de Pesquisas Físicas (CBPF))

16:15 Remarks on nonlocality: Field theories and gravitation - Rodrigo Bufalo (UFLA)
16:40 Zamolodchikov's c function in the study of the stability of non-Abelian topological phases - Carlos Hernaski (Universidade Tecnológica Federal do Paraná)
Zamolodchikov's c function in the study of the stability of non-Abelian topological phases
- Carlos Hernaski (Universidade Tecnológica Federal do Paraná)
16:40 - 17:15
We use the Zamolodchikov's c function to study the stability of non-Abelian 2+1 dimensional topological phases of matter. We show in the seminar that we can construct an interpolating function that connects UV fixed points with interesting classes of topological spin liquid phases of matter in the IR regime.
17:15 Intervalo
Intervalo
17:15 - 17:20
17:20 Some Higher-Derivative Theories in Practical Terms - Ronaldo Thibes (Universidade Estadual do Sudoeste da Bahia)
Some Higher-Derivative Theories in Practical Terms
- Ronaldo Thibes (Universidade Estadual do Sudoeste da Bahia)
17:20 - 17:55
Since the final decades of the last century it has become clear that quantum field theory (QFT) represents a major framework for describing fundamental nature phenomena. The generalization of this framework for models containing higher-order derivative terms, however an old subject, still poses itself as a challenging one with many open problems and subtleties. The relevance of higher-derivative models relies not just on abstract mathematical points, actually many modern approaches to quantum gravity allow for higher-order derivatives, besides its importance on the description of interacting models with room for more degrees of freedom. We present here a brief overview of some specific aspects of higher-derivative theories. Rather than entering on the fundamentals of important open issues such as unitarity, positiveness and causality, we focus instead on particular historical facts and pinpoint a few practical feasible issues present in recent published works. Starting from the 1950 well-known Pais-Uhlenbeck groundbreaking paper, we discuss the higher-derivative models of Bopp-Podolsky, Lee-Wick, Pais-Uhlenbeck oscillator and possible higher-order generalizations for the Klein-Gordon action. By performing a comparative analysis among those models, we show that it is possible to infer properties and behavior for ones from the others, in this way shedding some light in the whole higher-derivative problem in QFT. The fourth-order Pais-Uhlenbeck oscillator is perhaps the simplest instance of a nontrivial and relevant higher-order model. Defined in the realm of quantum mechanics, it comes from the quantization of a fourth-order classical oscillator system and already displays the mains characteristics of its more robust cousin models in QFT. The Boppy-Podolsky and Lee-Wick models describe higher-derivative theories with vector gauge fields. We discuss the gauge-fixing process for those models and show how clever gauge choices can lead to neat handy propagators which can considerably simplify perturbative calculations. Concerning higher-order generalizations for the Klein-Gordon equation, we discuss the classical solutions for a recently proposed natural action containing arbitrarily higher powers of the d'Alembertian operator acting on a scalar field. Along with the mentioned comparative analysis among those models, we also consider the interesting approach of reducing the order of the derivatives at the cost of introducing extra variables, weighing pros and cons, and provide a few arguments regarding their physical interpretation. To concretely illustrate the ideas, we discuss a reduced-order version for the Bopp-Podolsky model which has appeared recently in the literature, with both advantages of lower-order derivatives and sensible physical interpretation in terms of massive and massless propagating modes.
17:55

17:55 - 18:15

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