An investigation is performed of the Lorentz-violating electrodynamics extracted from the renormalizable sector of the general Lorentz-and CPT-violating standard-model extension. Among the unconventional properties of radiation arising from Lorentz violation is birefringence of the vacuum. Limits on the dispersion of light produced by galactic and extragalactic objects provide bounds of 3ϫ10 Ϫ16 on certain coefficients for Lorentz violation in the photon sector. The comparative spectral polarimetry of light from cosmologically distant sources yields stringent constraints of 2ϫ10 Ϫ32 . All remaining coefficients in the photon sector are measurable in high-sensitivity tests involving cavity-stabilized oscillators. Experimental configurations in Earth-and space-based laboratories are considered that involve optical or microwave cavities and that could be implemented using existing technology.

A general formalism is presented for violations of Lorentz and CPT symmetry in the neutrino sector. The effective Hamiltonian for neutrino propagation in the presence of Lorentz and CPT violation is derived, and its properties are studied. Possible definitive signals in existing and future neutrino-oscillation experiments are discussed. Among the predictions are direction-dependent effects, including neutrino-antineutrino mixing, sidereal and annual variations, and compass asymmetries. Other consequences of Lorentz and CPT violation involve unconventional energy dependences in oscillation lengths and mixing angles. A variety of simple models both with and without neutrino masses are developed to illustrate key physical effects. The attainable sensitivities to coefficients for Lorentz violation in the Standard-Model Extension are estimated for various types of experiments. Many experiments have potential sensitivity to Planck-suppressed effects, comparable to the best tests in other sectors. The lack of existing experimental constraints, the wide range of available coefficient space, and the variety of novel effects imply that some or perhaps even all of the existing data on neutrino oscillations might be due to Lorentz and CPT violation.

The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentz- and CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete characterization of the coefficients for Lorentz violation for all mass dimensions via a decomposition using spin-weighted spherical harmonics. The resulting nine independent sets of spherical coefficients control birefringence, dispersion, and anisotropy. We discuss the restriction of the general theory to various special models, including among others the minimal Standard-Model Extension, the isotropic limit, the case of vacuum propagation, the nonbirefringent limit, and the vacuum-orthogonal model. The transformation of the spherical coefficients for Lorentz violation between the laboratory frame and the standard Sun-centered frame is provided. We apply the results to various astrophysical observations and laboratory experiments. Astrophysical searches of relevance include studies of birefringence and of dispersion. We use polarimetric and dispersive data from gamma-ray bursts to set constraints on coefficients for Lorentz violation involving operators of dimensions four through nine, and we describe the mixing of polarizations induced by Lorentz and CPT violation in the cosmic-microwave background. Laboratory searches of interest include cavity experiments. We present the theory for searches with cavities, derive the experiment-dependent factors for coefficients in the vacuum-orthogonal model, and predict the corresponding frequency shift for a circular-cylindrical cavity.Comment: 58 pages two-column REVTeX, accepted in Physical Review

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 3 3 10 232 .

The behavior of fermions in the presence of Lorentz and CPT violation is studied. Allowing for operators of any mass dimension, we classify all Lorentz-violating terms in the quadratic Lagrange density for free fermions. The result is adapted to obtain the effective hamiltonian describing the propagation and mixing of three flavors of left-handed neutrinos in the presence of Lorentz violation involving operators of arbitrary mass dimension. A characterization of the neutrino coefficients for Lorentz violation is provided via a decomposition using spin-weighted spherical harmonics. The restriction of the general theory to various special cases is discussed, including among others the renormalizable limit, the massless scenario, flavor-blind and oscillation-free models, the diagonalizable case, and several isotropic limits. The formalism is combined with existing data on neutrino oscillations and kinematics to extract a variety of measures of coefficients for Lorentz and CPT violation. For oscillations, we use results from the short-baseline experiments LSND and MiniBooNE to obtain explicit sensitivities to effects from flavor-mixing Lorentz-violating operators up to mass dimension 10, and we present methods to analyze data from long-baseline experiments. For propagation, we use time-of-flight measurements from the supernova SN1987A and from a variety of experiments including MINOS and OPERA to constrain oscillation-free Lorentz-violating operators up to mass dimension 10, and we discuss constraints from threshold effects in meson decays anď Cerenkov emission.

The theoretical description of fermions in the presence of Lorentz and CPT violation is developed. We classify all Lorentz-and CPT-violating and invariant terms in the quadratic Lagrange density for a Dirac fermion, including operators of arbitrary mass dimension. The exact dispersion relation is obtained in closed and compact form, and projection operators for the spinors are derived. The Pauli hamiltonians for particles and antiparticles are extracted, and observable combinations of operators are identified. We characterize and enumerate the coefficients for Lorentz violation for any operator mass dimension via a decomposition using spin-weighted spherical harmonics. The restriction of the general theory to various special cases is presented, including isotropic models, the nonrelativistic and ultrarelativistic limits, and the minimal Standard-Model Extension. Expressions are derived in several limits for the fermion dispersion relation, the associated fermion group velocity, and the fermion spin-precession frequency. We connect the analysis to some other formalisms and use the results to extract constraints from astrophysical observations on isotropic ultrarelativistic spherical coefficients for Lorentz violation.

We consider neutrino oscillations in the minimal Standard-Model Extension describing general Lorentz and CPT violation. Among the models without neutrino mass differences is one with two degrees of freedom that reproduces most major observed features of neutrino behavior. DOI: 10.1103/PhysRevD.70.031902 PACS number͑s͒: 11.30.Cp, 11.30.Er, 14.60.Pq Quantum physics and gravity are believed to combine at the Planck scale, m P Ӎ10 19 GeV. Experimentation at this high energy is impractical, but existing technology could detect suppressed effects from the Planck scale, such as violations of relativity through Lorentz or CPT breaking ͓1͔. At experimentally accessible energies, signals for Lorentz and CPT violation are described by the Standard-Model Extension ͑SME͒ ͓2͔, an effective quantum field theory based on the Standard Model of particle physics. The SME incorporates general coordinate-independent Lorentz violation.The character of the many experiments designed to study neutrino oscillations ͓3͔ makes them well suited for tests of Lorentz and CPT symmetry. The effects of Lorentz violation on propagation in the vacuum can become more pronounced for light particles, and so small effects may become observable for large baselines. Applying this idea to photons has led to the best current sensitivity on any type of relativity violation ͓4͔.In this work, we study the general neutrino theory given by the minimal renormalizable SME ͓2͔. In this setup, as in the usual minimal Standard Model, SU(3)ϫSU(2)ϫU(1) symmetry is preserved, the right-handed neutrino fields decouple and so are unobservable, and there are no neutrino mass differences. The neutrino behavior is contained in the termswhere the first term is the usual Standard-Model kinetic term for the left-handed doublets L a , with index a ranging over the three generations e, , . The coefficients for Lorentz violation are (a L ) ab , which has mass dimension one and controls the CPT violation, and (c L ) ab , which is dimensionless. It is attractive to view these coefficients as arising from spontaneous violation in a more fundamental theory ͓5͔, but other origins are possible ͓1͔. The Lorentz-violating terms in Eq. ͑1͒ modify both interactions and propagation of neutrinos. Any interaction effects are expected to be tiny and well beyond existing sensitivities. In contrast, propagation effects can be substantial if the neutrinos travel large distances. The time evolution of neutrino states is controlled as usual by the effective Hamiltonian (h eff ) ab extracted from Eq. ͑1͒. The construction of (h eff ) ab is complicated by the unconventional time-derivative term but can be performed following the procedure in Ref. ͓6͔. We findTo leading order, the 4-momentum p is p ϭ(͉p͉;Ϫp). The analysis of neutrino mixing proceeds along the usual lines. We diagonalize (h eff ) ab with a 3ϫ3 unitary matrix U eff , h eff ϭU eff † E eff U eff , where E eff is a 3ϫ3 diagonal matrix. There are therefore two energy-dependent eigenvalue differences and hence two independent oscillatio...

The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.Comment: 12 page