Finite-group gauge theories on lattices as Hamiltonian systems with constraints

• URL: http://arxiv.org/abs/2206.09775v6
• Date: Sat, 25 Mar 2023 02:35:50 GMT
• Title: Finite-group gauge theories on lattices as Hamiltonian systems with constraints
• Authors: M. F. Araujo de Resende
• Abstract summary: lattice gauge theories are defined on $ n $-dimensional lattices by using finite gauge groups. We show how they can be interpreted as a Hamiltonian system with constraints, analogous to what happens with the classical (continuous) gauge (field) theories.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with constraints, analogous to what happens with the classical (continuous) gauge (field) theories. As this interpretation is not usually explored in the literature that discusses/introduces the concept of lattice gauge theory, but some recent works have been exploring Hamiltonian models in order to support some kind of quantum computation, we use this interpretation to, for example, present a brief geometric view of one class of these models: the Kitaev Quantum Double Models.

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