2013•International Journal of Geometric Methods in Modern PhysicsRequires access

GRADED LAGRANGIAN FORMALISM

G. Sardanashvily

Abstract

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems, characterized by hierarchies of non-trivial higher-order Noether identities and gauge symmetries. This is a general case of classical field theory and Lagrangian non-relativistic mechanics.

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Key concepts: Noether's theorem, Lagrangian, Formalism (music), Lagrangian system, Gauge symmetry, Degenerate energy levels, Homogeneous space, Inverse problem for Lagrangian mechanics