Correlation Functions of a Charged Scalar Field in the Background of Noncommutative U(1) Gauge Field - Solovyov, A. (Ukrainian Journal of Physics, 2022)
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.