Canonical Noether symmetries and commutativity properties for gauge systems

TL;DR

This paper characterizes canonical Noether symmetries in gauge systems by examining their commutation relations with evolution operators across different formalisms, enhancing understanding of symmetries in singular Lagrangian systems.

Contribution

It provides new characterizations of canonical Noether symmetries using commutation relations in phase space, velocity space, and through linking evolution operators.

Findings

Symmetries characterized via commutation relations

Unified approach across phase and velocity spaces

Improved understanding of gauge system symmetries

Abstract

For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate characterizations are given in phase space, in velocity space, and through an evolution operator that links both spaces.