Peter Tsimiklis | Applied Math, University of Waterloo
Discretization of 3+1D BF Theory Featuring Edgemodes
The first step in the quantization of gravity is the discretization of spacetime. In this work, I focus on the discretization of the symplectic structure of 3+1 dimensional BF theory, a topological theory from which general relativity can be recovered by adding a constraint. The discretization step involves subdividing a spatial slice of a manifold while encoding curvature and torsion as defects along the edges and vertices. Such a decomposition introduces extra degrees of freedom on the boundaries of the subdivisions, called edgemodes. Edgemodes restore gauge invariance which is broken by the introduction of boundaries and have been known to manifest with particle-like features.
In this talk, I will review the framework for the discretization process which has been established for 2+1 dimensional gravity and attempt to describe its generalization to 3+1 dimensional theory.