Logo image
Back
Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
Journal article   Open access   Peer reviewed

Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

Yannick Meurice
Physical review. D, Particles, fields, gravitation, and cosmology, Vol.102(1), p.1
07/01/2020
DOI: 10.1103/PhysRevD.102.014506
url
https://doi.org/10.1103/PhysRevD.102.014506View
Published (Version of record) Open Access

Abstract

We show that standard identities and theorems for lattice models with U(1) symmetry get reexpressed discretely in the tensorial formulation of these models. We also explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors. We further construct a gauge-invariant transfer matrix in arbitrary dimensions, show the equivalence with its gauge-fixed version in a maximal temporal gauge, and explain how a discrete Gauss's law is always enforced. Moreover, we propose a noise-robust way to implement Gauss's law in arbitrary dimensions, and we reformulate Noether's theorem for global, local, continuous, or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy. We discuss semiclassical approximations for classical solutions with periodic boundary conditions in two solvable cases, and we show the correspondence of their weak coupling limit with the tensor formulation after Poisson summation. Finally, we briefly discuss connections with other approaches and implications for quantum computing.
 Astronomy & Astrophysics Physical Sciences Physics Physics, Particles & Fields Science & Technology

Details

Metrics

6 Record Views
10 Times Cited - Web of Science
Logo image