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

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.

arXiv comment17 pages, to be published in Phys. Rev. D

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• First class models from linear and nonlinear second class constraints
• Five-Dimensional Mechanics as the Starting Point for the Magueijo-Smolin Doubly Special Relativity
• Classical gauge principle -- From field theories to classical mechanics
• To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models
• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal