Källén-Lehmann representation of noncommutative quantum electrodynamics

Abstract

Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some attention to the quantization of NC field theory on lower dimensions and look closely at the issue of dynamical mass generation to the gauge field. This work encompasses the quantization of the two-dimensional massive quantum electrodynamics and three-dimensional topologically massive quantum electrodynamics. We begin by addressing the problem on a general dimensionality making use of the perturbative Seiberg-Witten map to, thus, construct a general action, to only then specify the problem to two and three dimensions. The quantization takes place through the Källén-Lehmann spectral representation and Yang-Feldman-Källén formulation, where we calculate the respective spectral density function to the gauge field. Furthermore, regarding the photon two-point function, we discuss how its infrared behavior is related to the term generated by quantum corrections in two dimensions, and, moreover, in three dimensions, we study the issue of nontrivial θ-dependent corrections to the dynamical mass generation.

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Cited by in corpus (4)

• Lorentz-violating effects in three-dimensional $QED$
• Higher derivative Chern-Simons extension in the noncommutative QED${}_3$
• Nonperturbative Aspects of the two-dimensional Massive Gauged Thirring Model
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes