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.

References in corpus (10)

• Lorentz symmetry breaking as a quantum field theory regulator
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• Seiberg--Witten Maps to All Orders
• On the question of deconfinement in noncommutative Schwinger Model
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• Endemic Infrared Divergences in QED3 at Finite Temperature
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Higher Derivative Operators in the Noncommutative Schwinger Model
• Determination of the propagator in QED3 by spectral function
• Noncommutative real scalar field theory in 2+1 dimensions at finite temperature

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