Master Equation for Lagrangian Gauge Symmetries

TL;DR

This paper derives a Hamiltonian-based differential equation for gauge symmetry generators, clarifying restrictions on gauge parameters and connecting Hamiltonian and Lagrangian methods, with applications to Yang-Mills theory.

Contribution

It introduces a simple Hamiltonian differential equation for gauge symmetry generators, unifying previous restrictions and linking Hamiltonian and Lagrangian frameworks.

Findings

Derived a differential equation for gauge generators

Reproduced known restrictions on gauge parameters

Applied the framework to Yang-Mills theory

Abstract

Using purely Hamiltonian methods we derive a simple differential equation for the generator of the most general local symmetry transformation of a Lagrangian. The restrictions on the gauge parameters found by earlier approaches are easily reproduced from this equation. We also discuss the connection with the purely Lagrangian approach. The general considerations are applied to the Yang-Mills theory.