Lagrangian symmetries and supersymmetries depending on derivatives. Conservation laws and cohomology

TL;DR

This paper explores advanced symmetries and supersymmetries in higher order Lagrangian systems, establishing conservation laws and cohomological properties relevant to BRST theory.

Contribution

It generalizes the theory of symmetries and conservation laws to include derivatives-dependent supersymmetries in complex geometric settings.

Findings

Formulation of the first variational formula for higher order systems

Derivation of conservation laws for generalized symmetries

Analysis of cohomology of nilpotent supersymmetries

Abstract

Motivated by BRST theory, we study generalized symmetries and supersymmetries depending on derivatives of dynamic variables in a most general setting. We state the first variational formula and conservation laws for higher order Lagrangian systems on fiber bundles and graded manifolds under generalized symmetries and supersymmetries of any order. Cohomology of nilpotent generalized supersymmetries are considered.