A note on gauge systems from the point of view of Lie algebroids
Glenn Barnich
TL;DR
This paper reframes irreducible gauge field theories as Lie algebroids within the variational bi-complex, clarifying how the gauge, global, and asymptotic symmetries fit into a BV/BRST cohomological framework. It develops Noether operators, the gauge algebroid, and the longitudinal differential, then bedrocks an off-shell description via antifields and ghosts using the Koszul–Tate resolution and master action. The work connects SUSY-like symmetry structures to conserved currents and reducibility parameters through local BRST cohomology, providing a unified geometric language for gauge theory and its charges, with implications for gravity and asymptotic symmetry analyses. Overall, it offers a coherent synthesis that links Lie algebroid geometry, BV formalism, and cohomological methods to comprehensively describe symmetries in Lagrangian field theories.
Abstract
In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic symmetries.