Defining Canonical Momenta for Discretised SU(2) Gauge Fields
Marco Garofalo, Tobias Hartung, Karl Jansen, Johann Ostmeyer, and Simone Romiti, Carsten Urbach
TL;DR
This paper develops a method to define canonical momenta for discretized SU(2) gauge fields within the Hamiltonian framework, analyzing the commutation relations to ensure consistency in a basis where gauge fields are diagonal.
Contribution
It introduces a novel approach to defining canonical momenta for SU(2) lattice gauge theories in a diagonal gauge basis, including explicit construction and validation.
Findings
Constructed explicit momenta for discretized SU(2) gauge fields
Analyzed the violation of fundamental commutation relations
Provided a basis where gauge field operators are diagonal
Abstract
In this proceeding contribution we discuss how to define canonical momenta for SU(N) lattice gauge theories in the Hamiltonian formalism in a basis where the gauge field operators are diagonal. For an explicit discretisation of SU(2) we construct the momenta and check the violation of the fundamental commutation relations.
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