Two-dimensional Lorentz-violating Chern–Simons-like action

E Passos,A.Yu Petrov

doi:10.1016/j.physletb.2008.03.053

Abstract

We demonstrate generation of the two-dimensional Chern–Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.

Highlights

During recent years, different aspects of possibility of the Lorentz symmetry breaking and its possible implications call high scientific interest
It is naturally to expect, that this term naturally arises in the process of dimensional reduction of the above-mentioned three-dimensional Lorentz-breaking term and, of the fourdimensional Lorentz-breaking term arising in electrodynamics [1] which was earlier shown [11] to give the three-dimensional Lorentz-breaking term from [9]
We will discuss different issues related to this term, that is, its generating via coupling to some spinor matter and the dispersion relations in theories involving such a term

Summary

INTRODUCTION

Different aspects of possibility of the Lorentz symmetry breaking and its possible implications call high scientific interest. A lot of new effects implied by the Lorentz symmetry breaking were discovered, such as ambiguity of finite quantum corrections [2, 3], birefringence of the electromagnetic waves in vacuum, generation of this term and of its non-Abelian generalization via different methods (some papers describing these results are given in [4, 5]). An example of the possible Lorentz-breaking term with no higher derivatives in three-dimensional space-time is given by the mixed scalar-vector term studied earlier in the context of Julia-Toulouse mechanism [9]. We will discuss different issues related to this term, that is, its generating via coupling to some spinor matter (both at zero and finite temperature) and the dispersion relations in theories involving such a term.

SCALAR FIELD MODEL WITH THE CHERN-SIMONS-LIKE TERM

GENERATION OF THE CHERN-SIMONS-LIKE TERM VIA RADIATIVE CORRECTIONS

FINITE TEMPERATURE CASE

NONCOMMUTATIVE FIELDS METHOD

SUMMARY