Abstract
In this paper, we study the quantum behavior of the noncommutative Jackiw-Pi model. After establishing the Becchi-Rouet-Store-Tyutin (BRST) invariant action, the perturbative renormalizability is discussed, allowing us to introduce the renormalized mass and gauge coupling. We then proceed to compute the one-loop correction to the basic 1PI functions, necessary to determine the renormalized parameters (mass and charge), next we discuss the physical behaviour of these parameters.
Highlights
Mass generation for quantum fields has always been an important subject extensively studied even after the establishment of the standard model by means of Higgs mechanism
On its own, mass generation is seen by a completely new optics when the dimensionality of spacetime is lowered to (1 þ 1) and (2 þ 1) dimensions. In such cases there is a compatibility between gauge symmetry and massive vector fields, where nonperturbative effects play an important role and topological terms are allowed, respectively
These (2 þ 1)-dimensional field models possess interesting mathematical structure in their solution, but rather they are well motivated by allowing a gauge field theoretical description of condensed matter phenomena, such as high-Tc superconductivity and quantum Hall effect, among other examples [4]
Summary
Mass generation for quantum fields has always been an important subject extensively studied even after the establishment of the standard model by means of Higgs mechanism. On its own, mass generation is seen by a completely new optics when the dimensionality of spacetime is lowered to (1 þ 1) and (2 þ 1) dimensions In such cases there is a compatibility between gauge symmetry and massive vector fields, where nonperturbative effects play an important role and topological terms are allowed, respectively. Using this method Jackiw and Pi have suggested a theory for massive vector fields, which is simultaneously gauge invariant and parity preserving, this is namely the Jackiw-Pi model [5,6] In this case, the two vector fields have opposite parity transformations, which generate a mass-gap through a mixed Chern-Simons-like term preserving parity; the parity transformation is defined to include a field exchange together with the coordinate reflection, and this is a symmetry of the doubled theory.
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