TL;DR
This paper reviews the relationship between Noether and topological charges in gauge theories, introduces a new variational formulation of gravity with local invariance, and discusses covariant methods for defining surface charges.
Contribution
It provides a comparative analysis of charges in gauge theories, extends the understanding of boundary contributions, and introduces a covariant approach to surface charges replacing traditional methods.
Findings
Boundary components require independent consideration.
Helicity and enstrophies can be recognized as Noether charges.
A covariant ansatz for gauge theory surface charges is analyzed.
Abstract
In this short review we compare the rigid Noether charges to topological gauge charges. One important extension is that one should consider each boundary component of spacetime independently. The argument that relates bulk charges to surface terms can be adapted to the perfect fluid situation where one can recognise the helicity and enstrophies as Noether charges. More generally a forcing procedure that increases for instance any Noether charge is demonstrated. In the gauge theory situation, the key idea can be summarized by one sentence: ``go to infinity and stay there''. A new variational formulation of Einstein's gravity is given that allows for local GL(D,R) invariance. The a priori indeterminacy of the Noether charges is emphasized and a covariant ansatz due to S. Silva for the surface charges of gauge theories is analysed, it replaces the (non-covariant) Regge-Teitelboim procedure.
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