We consider the lightlike spontaneous Lorentz invariance violation (SLIV) appearing through the zero "length-fixing" constraint put on a gauge vector field, $A_{μ}A^{μ}=0$, and discuss its physical consequences in the framework of a conventional QED and beyond. Again, as in the timelike and spacelike SLIV cases, $A_{μ}A^{μ}=\pm M_{A}^{2}$ ($M_{A}$ is a scale of SLIV), while this constraint leads to an emergence of the Nambu-Goldstone modes collected in physical photon, the SLIV itself is still left unobservable unless gauge invariance in the theory is broken. At the same time, a crucial difference with the two former cases is that the asymmetrical vacuum corresponding to the lightlike Lorentz violation appears infinitely degenerated with all other vacua including the symmetrical one. We show that this degeneracy can be lifted out by introducing an extra gauge vector field being sterile with respect to an ordinary matter, though having some potential couplings with the basic $A_{μ}$ field. A slight mixing of them makes the underlying gauge invariance to be partially broken due to which physical Lorentz invariance occurs broken as well. This may cause a variety of the Lorentz violating processes some of which are briefly discussed.
Stringent limits on the Myers-Pospelov timelike parameter for photons $ξ<10^{-15}$ coming from astrophysical tests suggest exploring more general preferred backgrounds, such as spacelike and lightlike. We take some steps in this direction. We allow the external four vector $n$ characterizing the Lorentz symmetry breaking to have arbitrary directions in spacetime. We study the consistency for the effective field theories in each privileged frame by demanding causality, stability and analyticity. When specializing to a timelike background we found runaway solutions leading to causality and unita…
We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncomm…
The general charge-conserving effective scalar field theory incorporating violations of Lorentz symmetry is presented. The dispersion relation is used to infer the effects of spin-independent Lorentz violation on point-particle motion. A large class of associated Finsler spaces is derived, and the properties of these spaces is explored.
The objection [arXiv:1103.0168] to my theorem [arXiv:hep-ph/0201258] that violation of $CPT$ symmetry implies violation of Lorentz covariance is based on a nonlocal model in which time-ordered products are not well defined. I used covariance of time-ordered products as the condition for Lorentz covariance; therefore the proposed objection is not relevant to my result.
In Lorentz- and CPT-violating effective field theories involving scalar and spinor fields, there exist forms of Lorentz violation that modify only the scalar-spinor Yukawa interaction vertices. These affect low-energy fermion and antifermion scattering processes through modifications to the nonrelativistic Yukawa potentials. The modified potentials involve novel combinations of momentum, spin, and Lorentz-violating background tensors.
Supersymmetric field theories can be constructed that violate Lorentz and CPT symmetry. We illustrate this with some simple examples related to the original Wess-Zumino model.
We report that a general principle of physical independence of mathematical background manifolds brings a replacement of common derivative operators by co-derivative ones. Then we obtain a new Lagrangian for the ordinary minimal standard model with supplementary terms containing the Lorentz invariance violation information measured by a new matrix, denoted as the Lorentz invariance violation matrix. We thus provide a new fundamental theory to study Lorentz invariance violation effects consistently and systematically.
Standard model with intrinsic Lorentz and CPT violations is proposed in a Finsler geometric framework. We present explicitly Lorentz and CPT--breaking Lagrangians of the matter fields and the gauge fields in locally Minkowski spacetime. The Lorentz invariance violation is found to be originated from the spacetime background deviating from the Minkowski one. Similarly, the CPT violation is determined by the behaviors of the locally Minkowski metric under the parity and time reversal operations. To help understanding phenomenologies, we compare the Finslerian model with the standard--model exten…
We discuss the issue of fermion mass hierarchies between lepton and quark families in toy models of dynamical generation of fermion masses through minimal Lorentz Invariance Violation. Realistic hierarchies in chiral theories necessitate an extended gauge structure, which includes both vector and axial-vector interactions.
We discuss the impact of a tiny Lorentz-violating $b^μ$ term on the one dimensional motion of a Dirac particle scattering on a rectangular barrier. We assume the experiment is performed in a particular inertial frame, where the components of $b^μ$ are assumed constants. The results show that Lorentz-violation modification to the transmission rate depends on the observer Lorentz nature of $b^μ$. For a spacelike or lightlike $b^μ$ the induced resonant frequency shift depends on the polarization, while for timelike $b^μ$ there is essentially no modification.
An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.
Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bou…
Infrared, optical, and ultraviolet spectropolarimetry of cosmological sources is used to constrain the pure electromagnetic sector of a general Lorentz-violating standard-model extension. The coefficients for Lorentz violation are bounded to less than 3x10^{-32}.
We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric Standard Model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultra--violet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications of dispersion relations at high energies thereby escaping constraints from astrophysical searches for Lorentz violation.
Neutrino oscillations provide an opportunity for sensitive tests of Lorentz invariance. This talk reviews some aspects of Lorentz violation in neutrinos and the prospect of testing Lorentz invariance in neutrino-oscillation experiments. A general Lorentz-violating theory for neutrinos is discussed, and some signals of Lorentz violation are identified.
We point out that equivalence principle violations, while not dynamically equivalent, produce the same kinematical effects as Lorentz invariance violations for particle processes in a constant gravitational potential. This allows us to translate many experimental bounds on Lorentz invariance violations into bounds on equivalence principle violations. The most stringent bound suggests that a postive signal in an Eötvös experiment may be at least seven orders of magnitude beyond current technology.
This talk outlines some results for gravitational theories with local Lorentz violation in the context of the Lorentz- and CPT-violating Standard-Model Extension.
Lorentz violation naturally leads to neutrino oscillations and provides an alternative mechanism that may explain current data. In this work, we discuss possible signals of Lorentz violation in neutrino-oscillation experiments.
Spectropolarimetry of distant sources of electromagnetic radiation at wavelengths ranging from infrared to ultraviolet are used to constrain Lorentz violation. A bound of 3x10^{-32} is placed on coefficients for Lorentz violation.
Vacuum birefringence is a signature of Lorentz-symmetry violation. Here we report on a recent search for birefringence in the cosmic microwave background. Polarization data is used to place constraints on certain forms of Lorentz violation.
In a model with Lorentz invariance violation implemented through modified dispersion relations, we estimate the rate for the decay process gamma -> 3 gamma and find that it provides a relevant bound on Lorentz invariance violation.
Solar-neutrino oscillations are considered using a massive model with perturbative Lorentz violation. The adiabatic approximation is used to calculate the effects of Lorentz violation to leading order. The results are more compact than previous work involving vacuum oscillations, and are accurate for small Lorentz-violating coefficients.
We consider bulk fields coupled to the graviton in a Lorentz violating fashion. We expect that the overly tested Lorentz symmetry might set constraints on the induced Lorentz violation in the brane, and hence on the dynamics of the interaction of bulk fields on the brane. We also use the requirement for Lorentz symmetry to constrain the cosmological constant observed on the brane.
Relating the effective Lorentz violation coefficients for composite particles to the coefficients for their constituent fields is a challenging problem. We calculate the Lorentz violation coefficients relevant to the dynamics of an alpha-particle in terms of proton and neutron coefficients. The alpha-particle coefficients would lead to anisotropies in the alpha-decays of nuclei, and because the decay process involves quantum tunneling, the effects of any Lorentz violations could be exponentially enhanced.
Existing experimental data for neutrino oscillations are consistent with Lorentz-violating massless neutrinos. This talk summarizes some aspects of neutrino oscillations from the perspective of Lorentz and CPT violation in effective quantum field theory.
This presentation discusses some of the signals for Lorentz violation potentially observable in atomic spectroscopy and clock-comparison experiments. The emphasis of the discussion is on how the angular-momentum quantum numbers of the states involved in the transition determine the properties of the possible sidereal variation of the transition frequency.
This talk provides a status report on CPT violation in neutral-meson oscillations, focusing on implications of the CPT- and Lorentz-violating standard-model extension.
A general introduction to Lorentz and CPT violation is presented. The observable effects of the breakdown of such fundamental symmetries in neutrinos are outlined and different experimental searches of some of the key signals of Lorentz violation are discussed. A novel powerful method to study model-independent neutrino oscillations is reviewed and then used to illustrate a new global model of neutrino oscillations based on Lorentz violation consistent with atmospheric, accelerator, reactor, and solar neutrino data.
Broken spacetime symmetries might emerge from a fundamental physical theory. The effective low-energy theory might be expected to exhibit violations of supersymmetry and Lorentz invariance. Some illustrative models which combine supersymmetry and Lorentz violation are described, and a superspace formulation is given.
The effects of quark-sector Lorentz violation on deep inelastic electron-proton scattering are studied. We show that existing data can be used to establish first constraints on numerous coefficients for Lorentz violation in the quark sector at an estimated sensitivity of parts in a million.
Bipartite Riemann-Finsler geometries with complementary Finsler structures are constructed. Calculable examples are presented based on a bilinear-form coefficient for explicit Lorentz violation.
Lorentz-violating extensions of the Wess-Zumino model have been formulated in superspace. The models respect a supersymmetry algebra and can be understood as arising from suitably modified superspace transformations.
Electromagnetic resonant cavities form the basis for a number modern tests of Lorentz invariance. The geometry of most of these experiments implies unsuppressed sensitivities to parity-even Lorentz violations only. Parity-odd violations typically enter through suppressed boost effects, causing a reduction in sensitivity by roughly four orders of magnitude. Here we discuss possible techniques for achieving unsuppressed sensitivities to parity-odd violations by using asymmetric resonators.
Electromagnetic resonant cavities form the basis of many tests of Lorentz invariance involving photons. The effects of some forms of Lorentz violation scale with cavity size. We investigate possible signals of violations in the naturally occurring resonances formed in the Earth-ionosphere cavity. Comparison with observed resonances places the first terrestrial constraints on coefficients associated with dimension-three Lorentz-violating operators at the level of 10^{-20} GeV.
The violation of Lorentz symmetry can arise in a variety of approaches to fundamental physics. For the description of the associated low-energy effects, a dynamical framework known as the Standard-Model Extension has been developed. This talk gives a brief review of the topic focusing on Lorentz violation through varying couplings.
Lorentz violation is a predicted phenomenon from the Planck scale physics. Although the three active massive neutrino framework with the Standard Model (SM), so-called the neutrino Standard Model (nuSM), is successful, series of signals not understood within the nuSM suggest neutrino physics may be the first place to see the physics beyond the SM, such as Lorentz violation. Especially, neutrino oscillations are the natural interferometer and they are sensitive to the Lorentz violation. The LSND oscillation signal was analyzed under the Standard Model Extension (SME) framework, and it was found…
Overview of spontaneous Lorentz and CPT breaking mechanism in the context of the standard model contributed to the proceedings for the Coral Gables meeting.
Space-based experiments offer sensitivity to numerous unmeasured effects involving Lorentz and CPT violation. We provide a classification of clock sensitivities and present explicit expressions for time variations arising in such experiments from nonzero coefficients in the Lorentz- and CPT-violating Standard-Model Extension.
We consider Lorentz violation in supersymmetric extensions of the standard model. We perform a spurion analysis to show that, in the simplest natural constructions, the resulting supersymmetry-breaking masses are tiny. In the process, we argue that one of the strongest bounds on Lorentz violation in the photon Lagrangian, which comes from the absence of birefringence from distant astrophysical sources, does not apply when Lorentz violation is parametrized by a single vector.
This contribution to the CPT'16 proceedings summarizes recent tests of Lorentz violation in the pure-gravity sector with cosmic rays and reviews recent progress in matter-gravity couplings.
Momentum dependence of quantum corrections with higher-dimensional Lorentz violation is examined in electrodynamics on orbifolds. It is shown that effects of the Lorentz violation are not decoupled at high energy scales. Despite the loss of the higher-dimensional Lorentz invariance, a higher-dimensional Ward identity is found to be fulfilled for one-loop vacuum polarization. This implies that gauge invariance may be prior to Lorentz invariance as a guiding principle in higher-dimensional field theory. As a universal application of electrodynamics, an extra-dimensional aspect for Furry's theore…
An overview of recent progress on testing Lorentz and CPT symmetry using Penning traps is presented. The theory of quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six is summarized. Dominant shifts in the cyclotron and anomaly frequencies of the confined particles and antiparticles due to Lorentz and CPT violation are derived. Existing results of the comparisons of charge-to-mass ratios and magnetic moments involving protons, antiprotons, electrons, and positrons are used to constrain various coefficients for Lorentz violation.
We review the basics of the two most widely used approaches to Lorentz violation - the Stardard Model Extension and Noncommutative Field Theory - and discuss in some detail the example of the modified spectrum of the synchrotron radiation. Motivated by touching upon such a fundamental issue as Lorentz symmetry, we ask three questions: What is behind the search for Lorentz violation? Is String Theory a physical theory? Is there an alternative to Supersymmetry?
The explicit one-loop renormalizability of the gluon sector of QCD with Lorentz violation is demonstrated. The result is consistent with multiplicative renormalization as the required counter terms are consistent with a single re-scaling of the Lorentz-violation parameters. In addition, the resulting beta functions indicate that the CPT-even Lorentz-violating terms increase with energy scale in opposition to the asymptotically free gauge coupling and CPT-odd terms. The calculations are performed at lowest-order in the Lorentz-violating terms as they are assumed small.
The explicit one-loop renormalizability of pure Yang-Mills theory with Lorentz violation is demonstrated. The result is consistent with multiplicative renormalization as the required counter terms are consistent with a single re-scaling of the Lorentz-violation parameters. In addition, the resulting beta functions indicate that the CPT-even Lorentz-violating terms increase with energy scale in opposition to the asymptotically free gauge coupling and CPT-odd terms. The calculations are performed at lowest-order in the Lorentz-violating terms as they are assumed small.
We derive a modified dispersion relation (MDR) in the Lorentz violation extension of quantum electrodynamics (QED) sector in the standard model extension (SME) framework. Based on the extended Dirac equation and corresponding MDR, we observe the resemblance of the Lorentz violation coupling with spin-gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in 2-flavor space in a 2-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a much stringent bound ($\backsim10^{-2…
In this talk, we explore the relation between smoothly varying couplings and Lorentz violation. Within the context of a supergravity model, we present an explicit mechanism that causes the effective fine-structure parameter and the effective electromagnetic $θ$ angle to acquire related spacetime dependences. We argue that this leads to potentially observable Lorentz violation and discuss some implications for the Standard-Model Extension.
This talk, given at CPT'13, showed Super-Kamiokande atmospheric-neutrino Monte Carlo sensitivity to Lorentz-violation effects using the perturbative model derived from the Standard-Model Extension.
This contribution to the CPT'16 meeting briefly highlights some of the recent progress in the phenomenology of Lorentz and CPT violation, with emphasis on research performed at the Indiana University Center for Spacetime Symmetries.
In recent years, the effects of Lorentz symmetry breaking in cosmology has attracted considerable amount of attention. In cosmological context several topics can be affected by Lorentz violation,e.g., inflationary scenario, CMB, dark energy problem and barryogenesis. In this paper we consider the cosmological particle creation due to Lorentz violation (LV). We consider an exactly solvable model for finding the spectral properties of particle creation in an expanding space-time exhibiting Lorentz violation. In this model we calculate the spectrum and its variations with respect to the rate and …
We analyze Doppler-effect experiments in terms of a general framework for violations of Lorentz symmetry: the Standard-Model Extension. These experiments are found to be sensitive to heretofore unprobed combinations of Lorentz-violation coefficients associated with protons and electrons. New bounds at the level of $10^{-11}$ and $10^{-8}$ for proton coefficients and $10^{-2}$ for electron coefficients emerge from a recent experiment.
Depending on deformed canonical anti-commutation relations, massless neutrino oscillation based on Lorentz invariance violation in non-commutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anti-commutation relations should satisfy the condition of new Moyal product and new non standard commutation relations. Furthermore, comparing the Lorentz Invariant Violation parameters $\mathit{A}$ in the previous studies with new Moyal product and new non standard commutation relations, we find that the orders of magnitud…
