Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics

Radiative corrections arising from Lorentz violation in the fermion sector induce a nonzero amplitude for vacuum photon splitting. At one loop, the on-shell amplitude acquires both CPT-even and CPT-odd contributions forbidden in conventional electrodynamics.Comment: 4 pages, minor wording changes, references added, accepted in Physical Review Letter

Gravity from Local Lorentz Violation

In general relativity, gravitational waves propagate at the speed of light, and so gravitons are massless. The masslessness can be traced to symmetry under diffeomorphisms. However, another elegant possibility exists: masslessness can instead arise from spontaneous violation of local Lorentz invariance. We construct the corresponding theory of gravity. It reproduces the Einstein-Hilbert action of general relativity at low energies and temperatures. Detectable signals occur for sensitive experiments, and potentially profound implications emerge for our theoretical understanding of gravity.Comment: 6 pages, accepted in General Relativity and Gravitatio

Neutrinos with Lorentz-violating operators of arbitrary dimension

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 and Cherenkov emission.Comment: 35 pages two-column REVTe

Classical kinematics for Lorentz violation

Classical point-particle relativistic lagrangians are constructed that generate the momentum-velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.Comment: 6 pages, accepted for publication in Physics Letters

Sensitivity of CPT Tests with Neutral Mesons

The sensitivity of experiments with neutral mesons to possible indirect CPT violation is examined. It is shown that experiments conventionally regarded as equivalent can have CPT reaches differing by orders of magnitude within the framework of a minimal CPT- and Lorentz-violating extension of the standard model.Comment: 4 pages REVTeX, published in Physical Review Letter

Stability, Causality, and Lorentz and CPT Violation

Stability and causality are investigated for quantum field theories incorporating Lorentz and CPT violation. Explicit calculations in the quadratic sector of a general renormalizable lagrangian for a massive fermion reveal that no difficulty arises for low energies if the parameters controlling the breaking are small, but for high energies either energy positivity or microcausality is violated in some observer frame. However, this can be avoided if the lagrangian is the sub-Planck limit of a nonlocal theory with spontaneous Lorentz and CPT violation. Our analysis supports the stability and causality of the Lorentz- and CPT-violating standard-model extension that would emerge at low energies from spontaneous breaking in a realistic string theory.Comment: 20 pages, accepted for publication in Physical Review

Radial Coulomb and Oscillator Systems in Arbitrary Dimensions

A mapping is obtained relating analytical radial Coulomb systems in any dimension greater than one to analytical radial oscillators in any dimension. This mapping, involving supersymmetry-based quantum-defect theory, is possible for dimensions unavailable to conventional mappings. Among the special cases is an injection from bound states of the three-dimensional radial Coulomb system into a three-dimensional radial isotropic oscillator where one of the two systems has an analytical quantum defect. The issue of mapping the continuum states is briefly considered.Comment: accepted for publication in J. Math. Phy

Self-Maintained Coherent Oscillations in Dense Neutrino Gases

We present analytical solutions to the nonlinear equations describing the behavior of a gas of neutrinos with two flavors. Self-maintained coherent flavor oscillations are shown to occur when the gas density exceeds a critical value determined by the neutrino masses and the mean neutrino energy in the gas. Similar oscillations may have occurred in the early Universe.Comment: To appear in Physical Review D, July 199

Spontaneous Lorentz Violation and Nonpolynomial Interactions

Gauge-noninvariant vector field theories with superficially nonrenormalizable nonpolynomial interactions are studied. We show that nontrivial relevant and stable theories have spontaneous Lorentz violation, and we present a large class of asymptotically free theories. The Nambu-Goldstone modes of these theories can be identified with the photon, with potential experimental implications.Comment: 10 pages, accepted in Physics Letters

Lorentz Violation and Short-Baseline Neutrino Experiments

A general discussion is given of signals for broken Lorentz symmetry in short-baseline neutrino experiments. Among the effects that Lorentz violation can introduce are a dependence on energy differing from that of the usual massive-neutrino solution and a dependence on the direction of neutrino propagation. Using the results of the LSND experiment, explicit analysis of the effects of broken Lorentz symmetry yields a nonzero value (3+/-1) x 10^{-19} GeV for a combination of coefficients for Lorentz violation. This lies in the range expected for effects originating from the Planck scale in an underlying unified theory.Comment: 4 pages REVTe