The topic of this conference school is General-Relativistic Gauge Field Theory: its mathematical foundations, its first principle conceptual and technical development, state-of-the-art applications, and model building. The event also features contributed oral contributions by young researchers.
Organizing Committee: Lucrezia Ravera (Politecnico di Torino, DISAT, Italy), Jordan François (University of Graz, Austria), Vincenzo Antonelli (Politecnico di Torino, DISMA, Italy)
The Scientific Program includes the following modules (18 hours of lectures in total):
- [Module DG, 4.5h], 3 lectures, by Jordan François (University of Graz, Austria);
- [Module AS, 4.5h], 3 lectures, by Marc Geiller (ENS de Lyon, CNRS, France);
- [Module SR, 4.5h], 3 lectures, by Lucrezia Ravera (Politecnico di Torino, Italy);
- [Module FA, 4.5h], 3 lectures, by Philipp Berghofer (University of Graz, Austria).
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Lectures DG
Three lectures on Bundle Differential Geometry (DG) of Gauge Field Theory, to provide the mathematical and geometric tools underpinning classical gauge theories: e.g., Ehresmann connection and Yang-Mills Gauge Field Theory, Cartan connection and gauge gravity, twisted connections on field space and anomalies, differential geometry of field space and gauge-fixing.
Some References: J. François, "Differential geometry of gauge theory: an introduction", PoS Modave 2020 (2021) 002; J. François, L. Ravera, "Cartan geometry, supergravity, and group manifold approach", Archivum Math. 60 (2024) 4, 243-281; M. J. D. Hamilton, "Mathematical Gauge Theory : With Applications to the Standard Model of Particle Physics", Universitext (2017), Springer; J. A. de Azcarraga, J. M. Izquierdo, "Lie groups, Lie algebras, cohomology and some applications in physics", Cambridge Monographs on Mathematical Physics (1995), CUP; R. W. Sharpe, "Differential Geometry: Cartan's Generalization of Klein's Erlangen Program", Springer (1997); A. Cap, J. Slovák, "Parabolic Geometries I: Background and General Theory", Mathematical Surveys and Monographs, Volume 154 (2009), AMS.
Topics of Module DG:
- Principal bundles
- Gauge group
- Ehresmann and Cartan connections
- Cartan geometry
- Yang-Mills and gravitational gauge theories
- Bundle geometry of field space
- Gauge-fixing
- Cocyclic forms and anomalies
- Field-dependent gauge transformations
- Variational principle
- Basic cohomology of field space
- Physical degrees of freedom
- Introduction to the Dressing Field Method
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Lectures AS
Three lectures on Asymptotic Symmetries (AS) in General Relativity and applications to gravitational (and electromagnetic) radiation and gravitational waves physics.
Some References: ...
Topics of Module AS:
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Lectures SR
Three lectures on Symmetry Reduction (SR) schemes – in particular, the Dressing Field Method (DFM) and its relational interpretation – in General-Relativistic Gauge Field Theory, including state-of-the-art model building and applications (among which, e.g., General Relativity, Supersymmetric Field Theories, etc.).
Some References: J. François, L. Ravera, "On the Meaning of Local Symmetries: Epistemic-Ontological Dialectics", Found. Phys. 55 (2025) no.3, 38; J. François, "The dressing field method for diffeomorphisms: a relational framework", J. Phys. A: Math. Theor. 57 (2024); J. François, L. Ravera, "Geometric relational framework for general-relativistic gauge field theories", Fortsch. Phys. 2024 (2024) 2400149; J. François, L. Ravera, "Mechanics as a general-relativistic gauge field theory, and Relational Quantization", arXiv:2510.19845; P. Berghofer, J. François, S. Friederich, H. Gomes, G. Hetzroni, A. Maas, R. Sondenheimer, "Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches", Elements in the Foundations of Contemporary Physics, Cambridge University Press (2023); J. François, "Artificial versus Substantial Gauge Symmetries: A Criterion and an Application to the Electroweak Model", Philosophy of Science, 86(3):472–496, 2019; P. Berghofer, J. François, "Dressing vs. fixing: On how to extract and interpret gauge-invariant content", Foundations of Physics, 54(6):72, 2024; P. Berghofer, J. François, L. Ravera, "What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers", [arXiv:2505.12876 [physics.hist-ph]]; J. François, L. Ravera, "There is no boundary problem", [arXiv:2504.20945 [gr-qc]]; J. D. Brown, K. V. Kuchar, "Dust as a standard of space and time in canonical quantum gravity", Phys. Rev. D 51, 5600 (1995); C. Rovelli, "GPS observables in general relativity", Phys. Rev. D 65, 044017 (2002); T. Frankel, "The Geometry of Physics: An Introduction", 3rd Ed., Cambridge University Press, Cambridge (2011); A. Komar, "Construction of a Complete Set of Independent Observables in the General Theory of Relativity", Phys. Rev. 111, 1182 (1958); P. G. Bergmann, A. Komar, "The coordinate group symmetries of general relativity", Int. J. Theor. Phys. 5, 15 (1972); J. François, L. Ravera, "Raising galaxy rotation curves via dressing", Phys. Rev. D 112, L081501; J. Attard, J. François, S. Lazzarini, "Weyl gravity and Cartan geometry", Phys. Rev. D 93, 085032 (2016); J. François, L. Ravera, "Reassessing the foundations of Metric-Affine Gravity", Eur. Phys. J. C 85, 902 (2025); J. François, L. Ravera, "Dressing fields for supersymmetry: the cases of the Rarita-Schwinger and gravitino fields", JHEP 07 (2024), 041; J. François, L. Ravera, "Off-shell supersymmetry via manifest invariance", Phys. Lett. B 868 (2025) 139633; J. François, L. Ravera, "Unconventional Supersymmetry via the Dressing Field Method", Phys. Rev. D 111 (2025) 12, 125022; J. François, L. Ravera, "Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework", Annalen der Physik 537, no. 9 (2025): 537, e00121; J. François, L. Ravera, "Relational bundle geometric formulation of non-relativistic quantum mechanics", Fortschr. Phys. 2025 (2025): e70040.
Topics of Module SR:
- Symmetry Reduction via the DFM and its relational interpretation
- Field-theoretic application to Maxwell theory, U(1) case plus complex scalar, Abelian Higgs model (Spontaneous Symmetry Breaking and the DFM)
- Application of the DFM to gravity plus scalar fields
- "Boundary problem" and diffeo-dressing
- Scalar coordinatization in general-relativistic physics
- Conformal gravity and dressing
- The case of Metric-Affine Gravity
- Gauge-invariance in supersymmetric field theory
- Matter-interaction supergeometric framework and the DFM
- Symmetry reduction in quantum theory
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Lectures FA
Three lectures on Foundational Aspects (FA) of General-Relativistic Gauge Field Theory, to allow a clearer understanding of the current state of general-relativistic physics and gauge theories, starting from first principles and conceptual analysis.
Some References: ...
Topics of Module FA:
- Philosophy of physics more generally, with a focus on the discussion of the nature of time and space in classical physics (Leibniz-Clarke debate)
- The Hole argument
- Gauge symmetries and gauge-invariant approaches
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Contributed Talks
T.B.A.
