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.

Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes

“…Noncommutative three-dimensional field theory, in particular gauge theory, can find application in the study of planar physics in condensed matter and statistical physics [19][20][21]. After this observation, various perturbative aspects of the noncommutative Chern-Simons theory have been studied [22][23][24][25][26][27], NC Maxwell-Chern-Simons theory [28,29] and NC QED 3 [30,31], as well as its supersymmetric extension [32], where deviations of known phenomena and interesting new properties have been uncovered.…”

Higher derivative Chern-Simons extension in the noncommutativeQED3

“…In fact, various studies in analyzing three-dimensional gauge theories defined in a noncommutative space-time have uncovered deviations of known phenomena and interesting new properties of these theories [10][11][12][13][14][15][16]. One of the most exploited features of a threedimensional gauge theory is that, in one side, if you started with a theory with massless fermionic fields interacting with Chern-Simons gauge fields, a mass for the fermionic fields is generated dynamically by radiative corrections; on the other side, if you started with a theory with massive fermionic fields interacting with an external gauge field, the Chern-Simons action is also induced by radiative corrections.…”

Lorentz-violating effects in three-dimensional QED

“…In this work we shall consider a particular scenario that suffices our interests, a low-dimensional field theory endowed with Lorentz-violating coupling, to analyze mainly whether the spacetime dimensionality may account to the outcome quantities. In fact, low-dimensional field theories were recognized, a long time ago, as serving as laboratories where important theoretical ideas are tested in a simple setting [14][15][16][17], specially on condensed matter systems; for instance, the quantum Hall effect [18]. Furthermore, including to that, the fact that a field theory defined in a three-dimensional spacetime contains a highly interesting inner structure, due to the odd spacetime dimensionality, it is rather natural to investigate as theoretical options: how the spacetime dimensionality accounts in the analysis upon the generation of Lorentz-violating terms, and whether the Lorentz-violating effects changes some known theoretical results.…”