Construction of non-Abelian gauge theories on noncommutative spaces. (English) Zbl 1099.81524

Summary: We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.


81T13 Yang-Mills and other gauge theories in quantum field theory
81T75 Noncommutative geometry methods in quantum field theory
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