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

Jurčo, B.; Möller, L.; Schraml, S.; Schupp, P.; Wess, J.

Eur. Phys. J. C, Part. Fields 21, No. 2, 383-388 (2001).

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.

MSC:

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

Keywords:

Gauge parameter expansion; star product; fundamental representation