Generalization of the extended Lagrangian formalism on a field theory and applications

Formalism of extended Lagrangian represents 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 nonlinear sigma model.