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Noncommutative $$U(1)$$ gauge theory from a worldline perspective. (English) Zbl 1388.81264
Summary: We study pure noncommutative $$U(1)$$ gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green’s function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.
##### MSC:
 81T13 Yang-Mills and other gauge theories in quantum field theory 83C65 Methods of noncommutative geometry in general relativity
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