Lorentz Symmetry Violation Research Articles

SNO: Recent new results

The Sudbury Neutrino Observatory (SNO), whose main purpose was to study the neutrinos produced in the Sun, demonstrated that neutrinos can change flavor and, thus, they are massive particles. SNO detected and recorded neutrino and cosmic ray interactions from 1999 to 2006 and several analyses have been completed in the past year using legacy data. We present the results of the most recent ones: the measurements of neutron production in atmospheric neutrino interactions and neutron production by cosmic muons, a search for Lorentz symmetry violation in neutrino oscillations and a search for neutrino decay. A few other analyses are ongoing and we comment about their goal and status.

Testing CPT Symmetry with Neutral K Mesons: A Review

The neutral kaon system is a very peculiar system that offers unique possibilities to perform precise tests of the CPT symmetry. The entanglement of neutral kaon pairs that are produced at a ϕ-factory opens up new ways and scenarios in order to test this fundamental discrete symmetry. In this paper, the results of the most recent and significant CPT tests are reviewed. Experiments have set stringent limits on the CPT-violating parameters of different phenomenological models, some of them associated to possible decoherence mechanisms or Lorentz symmetry violation which might be justified in a quantum gravity framework. The present results show no violation of CPT symmetry, while their accuracy in some cases reaches the interesting level at which–in the most optimistic scenarios–quantum gravity effects might show up.

The local Lorentz symmetry violation and Einstein equivalence principle

Lorentz symmetry violation (LV) was recently proposed to be testable with a new method, in which the effect of the violation is described as a certain local interaction Shaniv et al (2018 Phys. Rev. Lett. 120 103202). We revisit this LV effect in the paper and show that it is not only local, but it also represents a classical violation according to the recent quantum formulation of the Einstein equivalence principle (EEP). Based on a harmonically trapped spin-1/2 atomic system, we apply the results of table-top experiments testing LV effect to estimate the corresponding violation parameter in the quantum formulation of EEP. We find that the violation parameter is indeed very small, as expected by the earlier theoretical estimation.

Top hadrons in Lorentz-violating field theory

If there is Lorentz symmetry violation in the $t$ quark sector of the standard model, changes to particles' dispersion relations might allow for the existence of stable top-flavored hadrons. Observations of the survival of high-energy $\gamma$-rays over astrophysical distances can be used to place one-sided constraints on certain linear combinations of Lorentz violation coefficients in the $t$ sector at the $\sim 10^{-4}$ level of precision.

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.

Relativistic Analogues of the Aharonov-Bohm Effect and the Landau Quantization with the Lorentz Symmetry Violation Determined by Azimuthal Electric Fields and a Fixed Vector Field

We analyse the behaviour of the Dirac field under the effects of the violation of the Lorentz symmetry determined by a fixed time-like vector background and azimuthal electric fields. We show, from the interaction of the Dirac particle with an azimuthal electric field (proportional to the inverse of the radial distance) and the fixed time-like vector field, that analogues of the Aharonov-Bohm effect can be obtained. Besides, from the interaction of the Dirac field with an azimuthal electric field (proportional to the radial distance) and the fixed time-like vector field, therefore, a relativistic analogue of the Landau quantization can be achieved.

Casimir energy and topological mass for a massive scalar field with Lorentz violation

A Lorentz symmetry violation aether-type theoretical model is considered to investigate the Casimir effect and the generation of topological mass associated with a self-interacting massive scalar fields obeying Dirichlet, Newman and mixed boundary conditions on two large and parallel plates. By adopting the path integral approach we found the effective potential at one- and two-loop corrections which provides both the energy density and topological mass when taken in the ground state of the scalar field. We then analyse how these quantities are affected by the Lorentz symmetry violation and compare the results with previous ones found in literature.

Black hole echoes

We consider a very simple model for gravitational wave echoes from black hole merger ringdowns which may arise from local Lorentz symmetry violations that modify graviton dispersion relations. If the corrections are sufficiently soft so they do not remove the horizon, the reflection of the infalling waves which trigger the echoes is very weak. As an example, we look at the dispersion relation of a test scalar field corrected by roton-like operators depending only on spatial momenta, in Gullstrand-Painlev\'e coordinates. The near-horizon regions of a black hole do become reflective, but only very weakly. The resulting ``bounces" of infalling waves can yield repetitive gravity wave emissions but their power is very small. This implies that to see any echoes from black holes we really need an egregious departure from either standard GR or effective field theory, or both. One possibility to realize such strong echoes is the recently proposed classical firewalls which replace black hole horizons with material shells surrounding timelike singularities.

Bounding CPT and Lorentz symmetry violations through ultra-high-energy cosmic rays

We review recent work on CPT and Lorentz violation in the context of the Standard-Model Extension. In particular, we show that, when CPT and Lorentz violation is present in the kinetic terms of any particle in the gauge boson or the lepton sector, this will generally lead to proton decay at sufficiently high energy. Using observational data from ultra-high energy cosmic rays, this has allowed to derive new bounds on the corresponding CPT and Lorentz-violation parameters.

Quantum aspects of the Lorentz symmetry violation on an electron in a nonuniform electric field

By focusing on the interface between quantum field theory and nonrelativistic quantum mechanics, based on a theory that goes beyond the Standard Model, we consider the hypothesis of having a privileged direction in the space-time. This hypothesis is made by considering a background of the Lorentz symmetry violation determined by a fixed space-like vector field. Then, we analyse quantum effects of this background on the interaction of a nonrelativistic electron with a nonuniform electric field produced by a uniform electric charge distribution.

Aharonov–Bohm-type effect in an attractive inverse-square potential induced by Lorentz symmetry breaking effects

We discuss the quantum effects on a neutral particle subject to an attractive inverse-square potential induced by effects of the Lorentz symmetry violation at a low energy scenario. We consider a background of the Lorentz symmetry violation determined by a time-like four-vector and a field configuration of crossed electric and magnetic fields. We show a particular case where bound state solutions can be obtained and an analogue of the Aharonov–Bohm effect for bound states exists.

A Spacetime Symmetry Approach to Relativistic Quantum Multi-Particle Entanglement

A Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, in m time and n space dimensions, is the group of pseudo-rotations of a pseudo-Euclidean space of signature (m, n). Accordingly, the Lorentz group SO(1, 3) is the common Lorentz transformation group from which special relativity theory stems. It is widely acknowledged that special relativity and quantum theories are at odds. In particular, it is known that entangled particles involve Lorentz symmetry violation. We, therefore, review studies that led to the discovery that the Lorentz group SO(m, n) forms the symmetry group by which a multi-particle system of m entangled n-dimensional particles can be understood in an extended sense of relativistic settings. Consequently, we enrich special relativity by incorporating the Lorentz transformation groups of signature (m, 3) for all m ≥ 2. The resulting enriched special relativity provides the common symmetry group SO(1, 3) of the (1 + 3)-dimensional spacetime of individual particles, along with the symmetry group SO(m, 3) of the (m + 3)-dimensional spacetime of multi-particle systems of m entangled 3-dimensional particles, for all m ≥ 2. A unified parametrization of the Lorentz groups SO(m, n) for all m, n ∈ N, shakes down the underlying matrix algebra into elegant and transparent results. The special case when (m, n) = (1, 3) is supported experimentally by special relativity. It is hoped that this review article will stimulate the search for experimental support when (m, n) = (m, 3) for all m ≥ 2.

Symmetries from locality. I. Electromagnetism and charge conservation

It is well known that a theory of the (i) Lorentz invariant and (ii) locally interacting (iii) two degrees of freedom of a massless spin 1 particle, the photon, leads uniquely to electromagnetism at large distances. In this work, we remove the assumption of (i) Lorentz boost invariance, but we still demand (ii) and (iii). We consider several broad classes of theories of spin 1, which in general explicitly violate Lorentz symmetry. We restrict to the familiar two degrees of freedom of the photon. We find that most theories lead to non-locality and instantaneous signaling at a distance. By demanding a mild form of locality (ii), namely that the tree-level exchange action is manifestly local, we find that the photon must still be sourced by a conserved charge with an associated internal symmetry. This recovers the central features of electromagnetism, although it does not by itself impose Lorentz boost symmetry. The case of gravitation dramatically improves the final conclusion and is reported in detail in our accompanying paper Part 2.

Semiclassical Approach of Lorentz Symmetry Breaking Effects at a Low Energy Scenario

From backgrounds of the Lorentz symmetry breaking implemented by the tensor $\left (K_{F}\right )_{\mu \nu \alpha \beta }$ , we analyze the effects of the Lorentz symmetry violation at a low energy scenario from a semiclassical point of view by using the Wentzel, Kramers and Brillouin approximation. We show that the interaction of a neutral particle with electric and magnetic fields in the background defined by the tensor $\left (K_{F}\right )_{\mu \nu \alpha \beta }$ yields attractive scalar potentials, and thus, bound state solutions to the Schrodinger equation can be obtained.

A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

We determine the effect of Lorentz invariance violation in the vacuum energy and stress between two parallel plates separated by a distance L, in the presence of a massive real scalar field. We parametrize the Lorentz-violation in terms of a symmetric tensor hμν that represents a constant background. Through the Green's function method, we obtain the global Casimir energy, the Casimir force between the plates and the energy density in a closed analytical form without resorting to perturbative methods. With regards to the pressure, we find that Fc(L)=F0(L˜)/−dethμν, where F0 is the Lorentz-invariant expression, and L˜ is the plate separation rescaled by the component of hμν normal to the plates, L˜=L/−hnn. We also analyze the Casimir stress including finite-temperature corrections. The local behavior of the Casimir energy density is also discussed.

Casimir effect in Lorentz-violating scalar field theory: A local approach

We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance $L$, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term $\lambda \left( u \cdot \partial \phi \right )^{2}$, where the parameter $\lambda$ and the background four-vector $u ^{\mu}$ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. We show that the energy density $\mathcal{E}_{C}$ (and hence the pressure) can be expressed in terms of the Lorentz-invariant energy density $\mathcal{E}_{0}$ as follows \begin{align} \mathcal{E}_{C} (L) = \sqrt{\frac{1-\lambda u_{n} ^{2}}{1 + \lambda u ^{2}}} \mathcal{E}_{0} (\tilde{L}) , \notag \end{align} where $\tilde{L} = L / \sqrt{1-\lambda u_{n} ^{2}}$ is a rescaled plate-to-plate separation and $u_{n}$ is the component of $\vec{{u}}$ along the normal to the plates. As usual, divergences of the local Casimir energy do not contribute to the pressure.

Lorentz symmetry violation in QCD and the frustration of asymptotic freedom

We study the effect of Lorentz symmetry violation (LSV) on the behavior at high energy of $SU(N)$ gauge theory with quarks in the fundamental representation. The approach is similar to that for QED treated in a previous paper. In contrast to QED, standard Lorentz invariant QCD is asymptotically free. Our aim is to explore the structure of the renormalization group at high energy and hence weak coupling without requiring the Lorentz symmetry breaking to be small. The simplest type of LSV leaves the theory invariant under a subgroup of the Lorentz group that preserves a (timelike) 4-vector. We examine this case in detail and find that asymptotic freedom is frustrated. That is, at sufficiently high energy, the running coupling constant attains a minimum value before increasing again, while the LSV parameter increases without bound.

Lorentz symmetry violation and accelerated expansion of the universe

Lorentz symmetry violation and accelerated expansion of the universe

On the Dirac oscillator subject to a Coulomb-type central potential induced by the Lorentz symmetry violation

We investigated the relativistic oscillator model for spin-1/2 fermionic fields, known as the Dirac oscillator, in a background of breaking the Lorentz symmetry governed by a constant vector field inserted in the Dirac equation by non-minimal coupling, where we proposed two possible scenarios of Lorentz symmetry violation which induce a Coulomb-type potential. Thus, in the search for solutions of bound states, we determine, analytically, the relativistic energy profile for the Dirac oscillator, where an interesting quantum effect arises: The frequency of the Dirac oscillator is determined by the quantum numbers of the system and the parameters that characterize the scenarios of Lorentz symmetry violation.

Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field

Inspired by the extension of the Standard Model, we analyzed the effects of the spacetime anisotropies on a massive Dirac field through a nonminimal CPT-odd coupling in the Dirac equation, where we proposed a possible scenario that characterizes the breaking of the Lorentz symmetry which is governed by a background vector field and induces a Landau-type quantization. Then, in order to generalize our system, we introduce a hard-wall potential and, for a particular case, we determine the energy levels in this background. In addition, at the nonrelativistic limit of the system, we investigate the effects of the Lorentz symmetry violation on thermodynamic aspects of the system.