Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

Magnetic moment generation from non-minimal couplings in a scenario with Lorentz-symmetry violation

This paper deals with situations that illustrate how the violation of Lorentz symmetry in the gauge sector may contribute to magnetic moment generation of massive neutral particles with spin- and spin-1. The procedure we adopt here is based on Relativistic Quantum Mechanics. We work out the non-relativistic regime that follows from the wave equation corresponding to a certain particle coupled to an external electromagnetic field and a background that accounts for the Lorentz-symmetry violation, and we thereby read off the magnetic dipole moment operator for the particle under consideration. We keep track of the parameters that govern the non-minimal electromagnetic coupling and the breaking of Lorentz symmetry in the expressions we get for the magnetic moments in the different cases we contemplate. Our claim is that the tiny magnetic dipole moment of truly-elementary neutral particles might signal Lorentz-symmetry violation.     

On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects

The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the Lorentz symmetry violation out of the Standard Model Extension. Thereby, we show that a Coulomb-type potential can be induced by Lorentz symmetry breaking effects and bound states solutions to the Klein–Gordon equation can be obtained. Further, we discuss the effects of this Coulomb-type potential on the confinement of the relativistic scalar particle to a linear confining potential by showing that bound states solutions to the Klein–Gordon equation can also be achieved, and obtain a quantum effect characterized by the dependence of a parameter of the linear confining potential on the quantum numbers {n,l}$\{n,l\}$ of the system.     

On the harmonic-type and linear-type confinement of a relativistic scalar particle yielded by Lorentz symmetry breaking effects

Based on the Standard Model Extension, we investigate relativistic quantum effects on a scalar particle in backgrounds of the Lorentz symmetry violation defined by a tensor field. We show that harmonic-type and linear-type confining potentials can stem from Lorentz symmetry breaking effects, and thus, relativistic bound state solutions can be achieved. We first analyse a possible scenario of the violation of the Lorentz symmetry that gives rise to a harmonic-type potential. In the following, we analyse another possible scenario of the breaking of the Lorentz symmetry that induces both harmonic-type and linear-type confining potentials. In this second case, we also show that not all values of the parameter associated with the intensity of the electric field are permitted in the search for polynomial solutions to the radial equation, where the possible values of this parameter are determined by the quantum numbers of the system and the parameters associated with the violation of the Lorentz symmetry.     

Relativistic Anandan quantum phase in the Lorentz violation background

We study the influence of a classical background based on the violation of the Lorentz symmetry on the relativistic Anandan quantum phase. We show that the choice of the Lorentz symmetry violation background provides an abelian contribution for the relativistic Anandan quantum phase.     

Relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

In this work, we discuss the relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry.     

On the influence of a Rashba-type coupling induced by Lorentz-violating effects on a Landau system for a neutral particle

We study a possible scenario of the Lorentz symmetry violation background that allows us to build an analogue of the Landau system for a nonrelativistic Dirac neutral particle interacting with a field configuration of crossed electric and magnetic fields. We also discuss the arising of analogues of the Rashba coupling, the Zeeman term and the Darwin term from the Lorentz symmetry breaking effects, and the influence of these terms on the analogue of the Landau system confined to a two-dimensional quantum ring. Finally, we show that this analogy with the Landau system confined to a two-dimensional quantum ring allows us to establish an upper bound for the Lorentz symmetry breaking parameters.     

Relativistic Anandan quantum phase and the Aharonov–Casher effect under Lorentz symmetry breaking effects in the cosmic string spacetime

From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the violation of the Lorentz symmetry and write an effective metric for the cosmic string spacetime. Then, we investigate the arising of an analogue of the Anandan quantum phase for a relativistic Dirac neutral particle with a permanent magnetic dipole moment in the cosmic string spacetime under Lorentz symmetry breaking effects. Besides, we analyse the influence of the effects of the Lorentz symmetry violation and the topology of the defect on the Aharonov–Casher geometric quantum phase in the nonrelativistic limit.     

Charged tensor matter fields and Lorentz symmetry violation via spontaneous symmetry breaking

We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z boson of the so-called mirror matter models.Received: 30 October 2003, Revised: 16 March 2004, Published online: 23 June 2004     

Lorentzian Goldstone modes shared among photons and gravitons

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, \(A_{\mu }^{2}=\pm M_{A}^{2}\) and \(H_{\mu \nu }^{2}=\pm M_{H}^{2}\) (\(M_{A}\) and \(M_{H}\) are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.     

Scalar Aharonov‐Bohm‐type effect induced by Lorentz symmetry breaking effects

A possible scenario of the Lorentz symmetry violation is discussed based on the arising of geometric quantum phases yielded by the effects of the Lorentz symmetry violation in the CPT‐even gauge sector of Standard Model Extension. Analogues of the Anandan quantum phase and the scalar Aharonov‐Bohm effect for a neutral particle [J. Anandan, Phys. Lett. A 138 , 347 (1989)] are obtained from the parity‐odd sector of the tensor . Moreover, we build quantum holonomies associated with the analogue of the Anandan quantum phase and discuss a possible analogy with the geometric quantum computation [A. Ekert et al., J. Mod. Opt. 47 , 2501 (2000)].

     

Superluminal neutrino and spontaneous breaking of Lorentz invariance

Generally speaking, the existence of a superluminal neutrino can be attributed either to re-entrant Lorentz violation at ultralow energy from intrinsic Lorentz violation at ultrahigh energy or to spontaneous breaking of fundamental Lorentz invariance (possibly by the formation of a fermionic condensate). Re-entrant Lorentz violation in the neutrino sector has been discussed elsewhere. Here, the focus is on mechanisms of spontaneous symmetry breaking.     

Rashba coupling induced by Lorentz symmetry breaking effects

The arising of a Rashba‐like coupling, a Zeeman‐like term and a Darwin‐like term induced by Lorentz symmetry breaking effects in the non‐relativistic quantum dynamics of a spin‐1/2 neutral particle interacting with external fields is studied. Moreover, the influence of a Rashba‐like coupling induced by a Lorentz symmetry violation background on the Tan–Inkson potential [W.‐C. Tan and J. C. Inkson, Semicond. Sci. Technol. 11 , 1635 (1996)] is discussed.     

Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

The full spectrum of two‐dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of graphene, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in graphene. Here, only one Lorentz‐violating parameter is considered, belonging to the scalar sector. The analytical methods developed in the context of 1+1 field theories are extended to explore the effect of the Lorentz symmetry breaking in the charge carrier density of two‐dimensional materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. These findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.     

On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background

We show for the first time that the induced parity-even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken, dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light-like cosmic anisotropy axial-vector or for a time-like one, when in the presence of a bare photon mass.     

Entropic information for travelling solitons in Lorentz and CPT breaking systems

In this work we group four research topics apparently disconnected, namely solitons, Lorentz symmetry breaking, supersymmetry, and entropy. Following a recent work (Gleiser and Stamatopoulos, 2012), we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang–Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are arbitrary. In this case, the CE selects the best value of the parameter in the model.     

Stability of symmetry breaking states in finite-size Dicke model with photon leakage

We investigate the finite-size Dicke model with photon leakage. It is shown that the symmetry breaking states, which are characterized by non-vanishing $〈\stackrel{?}{a}〉\ne 0$ and correspond to the ground states in the superradiant phase in the thermodynamic limit, are stable, while the eigenstates of the isolated finite-size Dicke Hamiltonian conserve parity symmetry. We introduce and analyze an effective master equation that describes the dynamics of a pair of the symmetry breaking states that are the degenerate lowest energy eigenstates in the superradiant region with photon leakage. It becomes clear that photon leakage is essential to stabilize the symmetry breaking states and to realize the superradiant phase without the thermodynamic limit. Our theoretical analysis provides an alternative interpretation using the finite-size model to explain results from cold atomic experiments showing superradiance with the symmetry breaking in an optical cavity.     

Isospin symmetry breaking within the HLS Model: A full (\rho, \omega, \phi) mixing scheme

We study the way isospin symmetry violation can be generated within the Hidden Local Symmetry (HLS) Model. We show that isospin symmetry breaking effects on pseudoscalar mesons naturally induces correspondingly effects within the physics of vector mesons, through kaon loops. In this way, one recovers all features traditionally expected from mixing and one finds support for the Orsay phase modelling of the amplitude. We then examine an effective procedure which generates mixing in the whole sector of the HLS Model. The corresponding model allows us to account for all two body decays of light mesons accessible to the HLS model in modulus and phase, leaving aside the and modes only, which raise a specific problem. Comparison with experimental data is performed and covers modulus and phase information; this represents 26 physics quantities successfully described with very good fit quality within a constrained model which accounts for SU(3) breaking, nonet symmetry breaking in the pseudoscalar sector and, now, isospin symmetry breaking. Received: 18 July 2001 / Revised version: 4 October 2001 / Published online: 21 November 2001     

Dimensional reduction of the Abelian Higgs Carroll-Field-Jackiw model

Taking as a starting point a Lorentz non-invariant abelian Higgs model defined in 1 + 3 dimensions, we carry out its dimensional reduction to D = 1 + 2, obtaining a new planar model composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background ) that imposes the Lorentz violation to the reduced model. The propagators of the scalar and massive gauge field are evaluated and the corresponding dispersion relations determined. Based on the poles of the propagators, a causality and unitarity analysis is carried out at tree level. We then show that the model is totally causal, stable and unitary.Received: 2 July 2004, Revised: 21 September 2004, Published online: 1 December 2004