Generalization of the Extended Lagrangian Formalism on a Field Theory and Applications

TL;DR

This paper extends the Lagrangian formalism to field theories with constraints, providing a systematic approach to identify local symmetries, demonstrated through examples like electrodynamics and Yang-Mills fields.

Contribution

It generalizes the extended Lagrangian formalism to field theories with first-class constraints, offering detailed methodology and applications.

Findings

Unified approach to local symmetries in field theories

Application to electrodynamics, Yang-Mills, and sigma models

Enhanced understanding of constraints in Hamiltonian formalism

Abstract

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field and non-linear sigma model.