On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

TL;DR

This paper extends the concept of quasi-local charges in Yang--Mills theories to arbitrary gauge groups, analyzing their limits and conservation properties at infinity, and clarifies conditions for their conservation in radiative configurations.

Contribution

It generalizes quasi-local charges to non-Abelian gauge theories with arbitrary gauge groups and examines their behavior at spatial and null infinity.

Findings

No conserved total charges or NP quantities in generic radiative configurations for semisimple gauge groups.

Conditions for conservation depend on field configurations and gauge group structure.

Explicit calculations for stationary solutions with various gauge groups.

Abstract

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.