Field-parametrization dependence of Dirac's method for constrained Hamiltonians with first-class constraints: failure or triumph? Non-covariant models

TL;DR

This paper explores how Dirac's method for constrained Hamiltonian systems depends on field parametrization, showing that in non-covariant models, choosing the right parametrization simplifies gauge symmetry analysis.

Contribution

It demonstrates that field-parametrization dependence can be leveraged to identify natural variables that simplify the Hamiltonian formulation of non-covariant gauge theories.

Findings

Field-parametrization dependence preserves covariance in covariant theories.

In non-covariant models, optimal parametrization reveals the simplest gauge symmetry.

Dirac's procedure can be tailored to improve gauge symmetry analysis.

Abstract

We argue that the field-parametrization dependence of Dirac's procedure, for Hamiltonians with first-class constraints not only preserves covariance in covariant theories, but in non-covariant gauge theories it allows one to find the natural field parametrization in which the Hamiltonian formulation automatically leads to the simplest gauge symmetry.