Extended Phase Space in General Gauge Theories

Understand

In a recent paper, it was shown that in diffeomorphism-invariant theories, Noether charges associated with a given codimension-2 surface become integrable if one introduces an extended phase space.

• In this paper we extend the notion of extended phase space to all gauge theories with arbitrary combinations of internal and spacetime local symmetries.
• We formulate this in terms of a corresponding Atiyah Lie algebroid, a geometric object derived from a principal bundle which features internal symmetries and diffeomorphisms on an equal footing.
• In this language, gauge transformations are understood as morphisms between Atiyah Lie algebroids that preserve the geometric structures encoded therein.