A comment on the topological phase for anti-particles in a Lorentz-violating environment

Abstract

Recently, a scheme to analyse topological phases in Quantum Mechanics by means of the nonrelativistic limit of fermions non-minimally coupled to a Lorentz-breaking background has been proposed. In this letter, we show that the fixed background, responsible for the Lorentz-symmetry violation, may induce opposite Aharonov-Casher phases for a particle and its corresponding antiparticle. We then argue that such a difference may be used to investigate the asymmetry for particle/anti-particle as well as to propose bounds on the associated Lorentz-symmetry violating parameters.PACS numbers: 11.30. Cp, 11.30.Er, 03.65.Bz The Standard Model of Particle Physics is based on Lorentz-and CP T -invariances as fundamental symmetries that have been confirmed in numerous experiments [1]- [5]. Actually, the invariance under the combined CP Ttransformation is a consequence of first principles of relativistic quantum field theory. The most immediate consequence of CP T symmetry is the equality of mass and lifetime for a particle and its corresponding antiparticle. The best tests in this direction come from the limits on the mass difference between K 0 and K 0 [3], high precision measurements of the anomalous magnetic moments of the electrons, positrons and mesons (confined in a Penning trap) [4], and clock-comparison experiments [5].Lorentz-violating theories are presently studied as a possible extension of the Standard Model of Particle Physics. This proposal has been pushed forward by Colladay and Kosteletcký [6], who devised a Standard Model Extension (SME) incorporating all tensor terms stemming from the spontaneous symmetry breaking of a more fundamental theory. In this case, an effective action breaks Lorentz symmetry at the particle frame, but keeps unaffected the SU (3) × SU (2) × U (1) gauge structure of the underlying fundamental theory. This fact is of relevance in that it indicates that the effective model may preserve some good properties of the original theory, like causality, unitarity and stability.In the context of gauge theories endowed with Lorentz violation, some efforts have been recently devoted to investigate interesting features of relativistic quantum-mechanical models involving the presence of fermions. Indeed, considering the Dirac equation enriched by of a sort of non-minimal coupling, significant consequences on the particle behavior has been observed, as pointed out in the works of ref. [7]. In these papers, the analysis of the non-relativistic regime of the Dirac equation has revealed that topological quantum phases are induced whenever the fermion field is coupled to the fixed background and the gauge field in a non-minimal way. More specifically, it has been found out that a neutral particle acquires a magnetic moment (induced by the background), which originates the Aharonov-Casher (AC) phase subject to the action of an external electric field [10]. It is worth stressing that the standard Aharonov-Casher phase is interpreted as a Lorentz change in * Electronic address:

Classical solutions for the Carroll-Field-Jackiw-Proca electrodynamics

“…This means that the Lorentz-violating background, when coupled to the gauge field as in Lagrangian (1), does not alter the electrostatic sector. Analysis of Maxwell equations (4,5,6) in the static regime reveals that this scenario remains true even in the presence of a non-null current. Hence, the scalar potential and electric field achieved here are the same for a point-like charge in uniform motion (stationary solution), once the current J does not contribute to A 0 .…”

“…In this scenario, a minuscule Lorentz violation at a lower energy scale (scrutinized into the framework of the SME) is to be read as a remanent effect of spontaneous Lorentz violation at Planck scale. Nowadays, Lorentz violation has been investigated in many different systems and purposes [3], involving also fermions [4], CPT and Lorentz-violating probing tests [5], topological phases [6], radiative corrections [7] and the gauge sector [8,9].…”

Lorentz symmetry breaking effects on relativistic EPR correlations

“…[110], one can find the current limits on the coefficients of the Lorentz symmetry violation. In recent years, Lorentz symmetry breaking effects have been investigated in the hydrogen atom [111], on the Rashba coupling [112,113], in a quantum ring [114], in Weyl semi-metals [115], in tensor backgrounds [116,117], in the quantum Hall effect [118], and geometric quantum phases [119][120][121].…”

Lorentz Violation, Möller Scattering, and Finite Temperature

“…This new nonminimal coupling term may be CPT-odd or CPT-even. There are various applications for both terms [15][16][17][18][19][20][21][22][23][24][25]. In this paper, the CPT-odd term is chosen to calculate the Lorentz violation correction to the electron-electron scattering, known as Möller scattering.…”