Lorentz symmetry breaking effects on relativistic EPR correlations
H. Belich, C. Furtado, K. Bakke
备注：
Accepted for publication in The European Physical Journal C. arXiv admin note: substantial text overlap with arXiv:1504.07432, arXiv:1504.07262, arXiv:1412.5080, arXiv:1506.00562
Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then, we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB ((Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations.
Some traces of a specific Lorentz symmetry breaking scenario in the ground state of the Hydrogen atom are investigated. It is used standard Rayleigh-Schrödinger perturbation theory in order to obtain the corrections to the the ground state energy and wave function. It is shown that an induced four-pole moment arises, due to the Lorentz symmetry breaking. The model considered is the one studied in reference Eur. Phys. J. C {\bf 74}, 2937 (2014), where the Lorentz symmetry is broken in the electromagnetic sector.
By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is investigated. It is shown that the Dirac equation can be written in terms of an effective metric and a relativistic geometric phase stems from the topology of the cosmic string spacetime and the Lorentz symmetry breaking effects. Further, the nonrelativistic limit of the Dirac equation is discussed and it is shown th…
In this book, we review various aspects of the Lorentz symmetry breaking, both classical and quantum ones, with the special interest to perturbative generation of Lorentz-breaking terms. We present impacts of Lorentz symmetry breaking in noncommutative and supersymmetric theories. Also, we discuss the problem of Lorentz symmetry breaking in a curved space-time. The book is closed with a review of experimental studies of Lorentz symmetry breaking.
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 lin…
In this paper, we consider the perturbative generation of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED within different approaches and discuss its ambiguities.
Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induced a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels.
In this paper, we consider the finite temperature behaviour of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED and demonstrate that its ambiguities whose presence has been shown earlier in the zero temperature case stay also at the finite temperature.
Within the superfield approach, we formulate the superfield supersymmetric aether-like Lorentz-breaking models, both in three- and in four-dimensional cases.
In this paper, we use gauge embedding procedure and master action approach to establish the equivalence between the self-dual and Maxwell-Chern-Simons models with Lorentz symmetry breaking. As a result, new kinds of Lorentz-breaking terms arise.
The four dimensional Lorentz-breaking finite and determined Chern-Simons like action is generated as a one loop perturbative correction via an appropriate Lorentz-breaking coupling of the gauge field with the spinor field. Unlike the known schemes of calculations, within this scheme this term is found to be regularization independent.
We discuss modifications to the concept of an ``antiparticle'', induced by a breakdown of the CPT symmetry at a fundamental level, realized within an extended class of quantum gravity models. The resulting loss of particle-antiparticle identity in the neutral-meson system induces a breaking of the EPR correlation imposed by Bose statistics. The latter is parametrized by a complex parameter controlling the amount of contamination by the ``wrong'' symmetry state. The physical consequences are studied, and novel observables of CPT-violation in $ϕ$ factories are proposed.
We study the vacuum solutions of a gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking (LSB), radial/temporal LSB and axial/temporal LSB. The purely radial LSB result corresponds to new black hole solutions. When possible, Parametrized Post-Newtonian (PPN) parameters are computed and observational boundaries used to constrain the Lorentz symmetry breaking scale.
The gauge-invariant Chern-Simons-type Lorentz- and CPT-breaking term is here reassessed and a spin-projector method is adopted to account for the breaking (vector) parameter. Issues like causality, unitarity, spontaneous gauge-symmetry breaking and vortex formation are investigated, and consistency conditions on the external vector are identified.
This paper is devoted to investigating the interactions between stationary sources of the electromagnetic field, in a model which exhibits explicit Lorentz-symmetry breaking due to the presence of a single background vector. We focus on physical phenomena that emerge from this kind of breaking and which have no counterpart in Maxwell Electrodynamics.
A four-dimensional Lorentz-breaking non-Abelian Chern-Simons like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the non-Abelian gauge field to the spinor field. This term is shown to be regularization dependent but nevertheless it can be found unambiguously in different regularization schemes at zero and finite temperature.
We consider new issues of duality in four-dimensional Lorentz-breaking field theories. In particular, we demonstrate that the arising of the aether-like Lorentz-breaking term is necessary in order for the 4D models to display the duality analog between the MCS and self-dual models in 3D. We further study the dispersion relations in both theories and discuss the physical contents of the models involved in this new dualilty.
It is shown the existence of a static self-dual semilocal vortex configuration for the Maxwell-Higgs system with a Lorentz-violating CPT-even term. The dependence of the vorticity upper limit on the Lorentz-break term is also investigated.
We demonstrate the generation of the CPT-even, aether-like Lorentz-breaking actions for the scalar and electromagnetic fields via their appropriate Lorentz-breaking coupling to spinor fields in three, four and five space-time dimensions. Besides, we show that the aether-like terms for the spinor field also can be generated as a consequence of the same couplings. Also we discuss the dispersion relations in the theories with aether-like Lorentz-breaking terms and find the tree-level effective (Breit) potential for fermion scattering and the one-loop effective potential corresponding to the actio…
The first one-loop higher-derivative contribution to the effective action of the Lorentz-breaking spinor QED is obtained and shown to be finite and ambiguous.
We present a Lorentz-breaking supersymmetric algebra characterized by a critical exponent $z$. Such construction requires a non trivial modification of the supercharges and superderivatives. The improvement of renormalizability for supersymmetric scalar QED is shown and the Kählerian effective potentials are calculated in different cases. We also show how the theory flows naturally to the Lorentz symmetric case at low energies.
In this paper, we describe the perturbative generation of the higher-derivative Lorentz-breaking terms for the gauge field, that is, the Myers-Pospelov term and the higher-derivative Carroll-Field-Jackiw term. These terms are explicitly calculated in the one-loop approximation and shown to be finite and ambiguous.
In this paper, we study the spontaneous Lorentz symmetry breaking for a four-dimensional massless four-fermion model. Our methodology is based on use of the rationalized propagator. We show that a bumblebee potential arises as a result of one-loop calculations and displays nontrivial minima. Also we demonstrate that a phase transition restoring Lorentz invariance can occur at a finite temperature.
In this work we derive the Lorentz-PCT-violating effective action for a fermion in a constant and uniform electromagnetic field using the Fock-Schwinger proper time method and extract the exact value of the coefficient of the nonperturbatively induced Chern-Simons term.
We consider the abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The occurence of the dynamic breaking of Lorentz symmetry at classical and one-loop level is described for massless and massive vector fields. This phenomenon appears to be the non-perturbative counterpart of the perturbative renormalizability and/or unitarity breaking in the chiral gauge theories.
One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu-Goldstone bosons is obtained.
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 we use the criterion for studying the violation of Lorentz symmetry is that the gauge symmetry should be preserved.
The propagation of electromagnetic waves in a Lorentz-symmetry violating scenario where there is a region of polarized vacuum is studied. It turns out that the photon field acquires an interesting polarization state, possibly useful to set up upper bounds in Lorentz-violating models at laboratory scales.
In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a non-commutative space-time. We show that, unlike in some recente analysis of quantum gravity effects, supersymmetry does not protect the theory from the large Lorentz violating effects arising from the loop corrections. We take advantage of the non-commutative Wess-Zumino model to illustrate this point.
A scenario is presented on how to shift the predicted cutoff in the cosmic ray spectrum at 10**20 eV, called the Greisen-Zatsepin-Kuzmin limit (GKZ), to larger energies without breaking the Lorentz invariance. The formulation is based on a pseudo-complex extension of standard field theory. The dispersion relation of particles can be changed, leading to a modification of the GKZ limit. Maximal shifts are determined.
In this work, we present two possible venues to accomodate the $K_{F}$-type Lorentz-symmetry violating Electrodynamics in an $N=1$-supersymmetric framework. A chiral and a vector superfield are chosen to describe the background that signals Lorentz-symmetry breaking. In each case, the $\ K_{μνκλ}$-tensor is expressed in terms of the components of the background superfield that we choose to describe the breaking. We also present in detail the actions with all fermionic partners of the background that determine $\ K_{μνκλ}$.
A method is presented for deducing classical point-particle Lagrange functions corresponding to a class of quartic dispersion relations. Applying this to particles violating Lorentz symmetry in the minimal Standard-Model Extension leads to a variety of novel lagrangians in flat spacetime. Morphisms in these classical systems are studied that echo invariance under field redefinitions in the quantized theory. The Lagrange functions found offer new possibilities for understanding Lorentz-breaking effects by exploring parallels with Finsler-like geometries.
We consider the two-point function of the gauge field in Lorentz-breaking theories with higher-derivative extension of the Dirac Lagrangian. We show that the Carroll-Field-Jackiw term naturally arises in this theory as a quantum correction being perfectly finite and thus displaying no ambiguities. Also, the finiteness of this term at low energy limit and the absence of large Lorentz violating corrections allows to avoid the fine-tuning problem.
In this work, we obtain bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present a new possible scenario of studying the Lorentz symmetry breaking effects on a nonrelativistic quantum system defined by a fixed space-like vector field parallel to the radial direction interacting with a uniform magnetic field along the z-axis. Furthermore, we also discuss the influence of a Coulomb-like potential induced by Lorentz symmetry violation effects on the two-dimensional harmonic oscillator…
In this paper, we study a CPT-even Lorentz-breaking extension of the scalar QED. For this theory, we calculate the one-loop lower-order contributions in the Lorentz-violating parameters to the two-point functions of scalar and gauge fields. We found that the two background tensors, coming from the two sectors (scalar and gauge) are mixed in the one-loop corrections both in finite and divergent parts. This shows that these two Lorentz-breaking terms cannot be studied in an isolated form. Besides, the results in the gauge sector are confirmed to be transversal.
We calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and, then, some examples of Lorentz-violating extensions of scalar QED. We observed, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz-symmetry is restored. Besides, the one-loop corrections to the effective potential in all the cases we studied depend on the background tensors responsible for the Lorentz symmetry violation. This have consequences in physical quantities l…
We extend a result by Ojima on spontaneous symmetry breaking of Lorentz boosts in thermal (KMS) states and show that it is in fact a special case in a more general class of examples of spontaneous symmetry breaking of Lorentz symmetry in relativistic many-body systems. Furthermore we analyse the nature of the corresponding Goldstone phenomenon and the type of Goldstone excitations (provided they have particle character).
In a 4D four-fermion model we study the dynamical restoration of Lorentz and CPT symmetries at finite temperature. We evaluate the gap equation both at zero and at finite temperature and observe that, depending on the parameters of the theory, there is a critical temperature at which the Lorentz and CPT symmetries are restored.
We study the spontaneous Lorentz symmetry breaking in a field theoretical model in (2+1)-dimension, inspired by string theory. This model is a gauge theory of an anti-symmetric tensor field and a vector field (photon). The Nambu-Goldstone (NG) boson for the spontaneous Lorentz symmetry breaking is identified with the unphysical massless photon in the covariant quantization. We also discuss an analogue of the equivalence theorem between the amplitudes for emission or absorption of the physical massive anti-symmetric tensor field and those of the unphysical massless photon. The low-energy effect…
We present an extension of the Randall--Sundrum model in which, due to spontaneous Lorentz symmetry breaking, graviton mixes with bulk vector fields and becomes quasilocalized. The masses of KK modes comprising the four-dimensional graviton are naturally exponentially small. This allows to push the Lorentz breaking scale to as high as a few tenth of the Planck mass. The model does not contain ghosts or tachyons and does not exhibit the van Dam--Veltman--Zakharov discontinuity. The gravitational attraction between static point masses becomes gradually weaker with increasing of separation and ge…
In this paper we discuss finiteness and ambiguities of the higher-derivative Lorentz-breaking terms in extended QED with a magnetic coupling at the finite temperature. We find that, beside of the higher-derivative Carroll-Field-Jackiw-like term and Myers-Pospelov term, many new terms arise in a finite temperature case, but most of them vanish in high temperature limit.
A scalar field can be inserted in Maxwell and/or Einstein theory to effect symmetry breaking. Consequences of such a modification are discussed. Possible dynamics for the scalar field are presented.
In this paper, we generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is demonstrated with use of the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical.
In this paper, we discuss the chiral anomaly in a Lorentz-breaking extension of QED which, besides the common terms that are present in the Standard Model Extension, includes some dimension-five nonminimal couplings. We find, using the Fujikawa formalism, that these nonminimal couplings induce new terms in the anomaly which depend on the Lorentz-violating parameters. Perturbative calculations are also carried out in order to investigate whether or not new ambiguous Carroll-Field-Jackiw terms are induced in the effective action.
In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined …
In a 4D chiral Thirring model we analyse the possibility that radiative corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By studying the effective potential, we verified that the chiral current $\barψγ^μ γ_5 ψ$ may assume a nonzero vacuum expectation value which triggers the Lorentz and CPT violations. Furthermore, by making fluctuations on the minimum of the potential we dynamically induce a bumblebee like model containing a Chern-Simons term.
This paper is dedicated to the study of interactions between stationary field sources for the linearized unimodular gravity or WTDIFF theory in a model which exhibits Lorentz symmetry breaking due to the presence of the linearized topological Chern-Simons term in $3 + 1$ dimensions, where the Lorentz symmetry breaking is caused by a single background vector $v^μ$. Since the background vector is very tiny, we treat it perturbatively up to second order and we focus on physical phenomena which have no counterpart in standard WTDIFF theory. We consider effects related to field sources describing p…
We consider the higher-derivative Lorentz-breaking extension of QED, where the new terms are the Myers-Pospelov-like ones in gauge and spinor sectors, and the higher--derivative CFJ term. For this theory, we study its tree-level dynamics, discuss the dispersion relation, and present one more scheme for its perturbative generation, including the finite temperature case. Also, we develop a method to study perturbative unitarity based on consistent rotation of the theory to Euclidean space. We use this method to verify explicitly that for special choices of the Lorentz-breaking vector, the unitar…
In this work we present nonlinear models in two-dimensional space-time of two interacting scalar fields in the Lorentz and CPT violating scenarios. We discuss the soliton solutions for these models as well as the question of stability for them. This is done by generalizing a model recently published by Barreto and collaborators and also by getting new solutions for the model introduced by them.
We discuss applications of the proper-time method in various minimal Lorentz violating modifications of QED and present new results obtained with its use. Explicitly. we calculate the complete one-loop Heisenberg-Euler effective action involving all orders in $F_{mn}$, for two of the most studied minimal Lorentz-violating extensions of QED, the one characterized by the axial vector $b^m$ and the one involving the second-rank constant tensor $c^{mn}$.
In this paper we study the one- and two-loop contribution to the free energy in QED with the Lorentz symmetry breaking introduced via constant CPT-even Lorentz-breaking parameters at the high temperature limit. We find the impact of the Lorentz-violating term for the free energy and carry out a numerical estimation for the Lorentz-breaking parameter.
The behaviour of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor $\left(K_{F}\right)_{μναβ}$. Then, by introducing a scalar potential as a modification of the mass term of the Klein-Gordon equation, it is shown that the Klein-Gordon equation in the cosmic string spacetime is modified by the effects of the Lorentz symmetry viola…
This paper is devoted to detailed investigations of free scalar field theory on $κ$-Minkowski space. After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations. We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.
In this paper we take into account the existence of Gribov copies in a four-dimensional Yang-Mills theory in the Landau gauge with an effective Lorentz symmetry breaking, induced by the Carroll-Field-Jackiw (CFJ) term. The self consistent gap equation of the Gribov parameter is properly derived and, provided observational bounds to the amplitude of the CFJ parameter in the $SU(2)$ gauge theory, a qualitative analysis of the Gribov parameter and of the poles of the propagator is developed.
This paper is dedicated to the study of interactions between external sources for the electromagnetic field in a model which exhibits Lorentz symmetry breaking. We investigate such interactions in the CPT-even photon sector of the Standard Model Extension (SME), where the Lorentz symmetry breaking is caused by a background tensor $K_{(F)αβστ}$. Since the background tensor is very tiny, we treat it perturbatively up to first order and we focus on physical phenomena which have no counterpart in Maxwell electrodynamics. We consider effects related to field sources describing point-like charges, s…
Spontaneous violation of Lorentz symmetry by the vacuum condensation of an antisymmetric $2$-tensor is considered. The coset construction for nonlinear realization of spacetime symmetries is employed to build the most general low-energy effective action for the Goldstone modes interacting with photons. We analyze the model within the context of the Standard-Model Extension and noncommutative QED. Experimental bounds for some parameters of the model are discussed, and we readdress the subtle issues of stability and causality in Lorentz non-invariant scenarios. Besides the two photon polarizatio…
