Lie Algebroids and the Geometry of Off-shell BRST

Understand

It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories.

• In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated bundles.
• This turns out to be a simple but elegant change, mathematically involving a quotient that removes spurious structure.
• The payoff is that the entire geometric structure involves only vector bundles over space-time, and we emphasize that familiar concepts such as BRST are built into the geometry, rather than appearing as adjunct structure.