Correlation Functions of a Charged Scalar Field in the Background of Noncommutative U(1) Gauge Field
DOI:
https://doi.org/10.15407/ujpe56.5.420Keywords:
-Abstract
We consider a complex charged scalar field coupled to a constant background non-commutative U(1) gauge field and calculate the correlation function of two gauge-invariant composite operators. This calculation illustrates an interplay between the gauge transformations in gauge theories on noncommutative spaces and a space-time geometry. We show that the noncommutative gauge invariance is restored for higher-order correlators, though the Green's function itself is not invariant. The correlation functions reveal a singular behavior in the case where the Seiberg–Witten map becomes singular; i.e., there is no equivalent commutative description.
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