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On quasi-local charges and Newman-Penrose type quantities in Yang-Mills theories. (English) Zbl 1222.83125

Summary: We generalize the notion of quasi-local charges, introduced by P. Tod for Yang-Mills fields with unitary gauge groups, to non-Abelian gauge theories with arbitrary gauge groups, 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.

MSC:

83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83C22 Einstein-Maxwell equations
81T13 Yang-Mills and other gauge theories in quantum field theory
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
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