Dynamical Lorentz symmetry breaking in 3D and charge fractionalization

Abstract

We analyze the breaking of Lorentz invariance in a 3D model of fermion fields self-coupled through four-fermion interactions. The low-energy limit of the theory contains various sub-models which are similar to those used in the study of the graphene or in the description of irrational charge fractionalization.Comment: 14 pages, 4 figures, revtex4; v2: minor modifications, typo corrections and some clarifications in section V, version published in PR

Three-dimensional Lorentz-violating action

“…Some issues related to this effective action were discussed in [9,[11][12][13][14]. It is natural to suggest that in the momentum space it can be represented as…”

“…The main reasons for it are the more simpler form and one-loop finiteness for almost all field theory models. The main results achieved in study of the Lorentz symmetry breaking in three-dimensional space-time are, first, generation of many Lorentz-breaking terms as a consequence of the spontaneous Lorentz symmetry breaking in the three-dimensional bumblebee model through a tadpole method with use of the reducible representation of the Dirac matrices [9], second, generalization of duality [10] for the Lorentz-breaking models implying in arising of new couplings between scalar, spinor and gauge fields [11], third, obtaining of new terms via dimensional reduction of the electrodynamics with the four-dimensional Lorentz-breaking Chern-Simons-like term [12]. In all these papers, a new mixed quadratic term involving both scalar and electromagnetic fields was shown to arise.…”

Lorentz violation bounds on Bhabha scattering

“…The interest in this issue appears in different contexts, such as supersymmetric models [5,6], noncommutative geometry [7], gravity and cosmology [8][9][10][11], high derivative models [12][13][14], renormalization [15][16][17][18] and scattering processes [19,20] in quantum electrodynamics (QED), condensed matter systems [21][22][23], and so on. Following these theoretical developments, many experimental tests on Lorentz-violating (LV) corrections have also been carried out and several constraints on LV parameters were established [24].…”

Chern-Simons terms in Lifshitz-like quantum electrodynamics

“…Beyond that, applications have been devised in diverse areas [6,[15][16][17][18]. Therefore, the study of the spacetime anisotropy in the theories involving the CS term is certainly relevant.…”