In 3d gravity with a cosmological constant, it has been shown that discretizing homogeneously curved geometries requires Poisson Lie group structures. This naturally appears when gluing 2d curved building blocks. At the quantum level, this building blocks are labeled with intertwiners defined in terms of quantum group representations.
To generalize this construction to the 4D case with a...
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. Operationally, subsystems are distinguished by physically accessible observables which are often implicitly specified relative to some external frame, such as the laboratory, or a background notion of locality. In absence of external relata (as in...
We consider the quantization of gravity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII).
We start from a holomorphic phase space formulation and consider holomorphic cylindrical wave functions over SL(2,C) connections. We use an overall phase ambiguity of the complex selfdual action to obtain...
We will report on the latest advances within the program of generalized spinfoam models using the framework of higher gauge theory. This framework, based on the idea of describing gauge symmetry using 2-groups, 3-groups and other higher-order categorical structures, has the advantage of treating both matter and gravity on an equal footing, which allows us to discuss matter-related topics such...
Computations in canonical loop quantum gravity are severely hindered by the graph-changing nature of the scalar Hamiltonian constraint. In fact, not even the action of this constraint on 4-valent spin-network vertices has been fully derived in the literature to date. For this reason, drastic approximations, such as graph-non-changing constraints, are usually implemented. In order to overcome...
By assuming matter can oscillate in proper time, we demonstrate that a matter field with proper time oscillations can mimic the properties of a bosonic field. The particles observed are proper time oscillators. The assumption also gives rise to properties that can reduce differences between quantum theory and general relativity, e.g., self-adjoint internal time operator and proper time...
Using properties of diffusion according to a quantum heat kernel constructed as an expectation over classical heat kernels on $S^1$, we probe the non-manifold-like nature of quantized space in a model of (1+1)-dimensional quantum gravity. By computing the mean squared displacement of a diffusing particle, we find that diffusion is anomalous, behaving similarly to that on a porous substrate,...
