In the context of conventional quantum field theory, we present a general Lorentz-violating extension minimal $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ standard model including $\mathrm{CPT}$-even and $\mathrm{CPT}$-odd terms. It can be viewed as low-energy limit physically relevant fundamental theory with Lorentz-covariant dynamics in which spontaneous Lorentz violation occurs. The has gauge invariance, energy-momentum...

Spontaneous $\mathrm{CPT}$ breaking arising in string theory has been suggested as a possible observable experimental signature neutral-meson systems. We provide theoretical framework for the treatment of low-energy effects spontaneous violation and attendant partial Lorentz breaking. The analysis is within context conventional relativistic quantum mechanics field four dimensions. use to develop $\mathrm{CPT}$-violating extension minimal standard model that could serve basis establishing...

The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic found to be physically equivalent a subset general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale noncommutativity parameter $(10\mathrm{TeV}{)}^{\ensuremath{-}2}$.

An investigation is performed of the Lorentz-violating electrodynamics extracted from renormalizable sector general Lorentz- and CPT-violating standard-model extension. Among unconventional properties radiation arising Lorentz violation birefringence vacuum. Limits on dispersion light produced by galactic extragalactic objects provide bounds $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ certain coefficients for in photon sector. The comparative spectral polarimetry...

Stability and causality are investigated for quantum field theories incorporating Lorentz $\mathrm{CPT}$ violation. Explicit calculations in the quadratic sector of a general renormalizable Lagrangian massive fermion reveal that no difficulty arises low energies if parameters controlling breaking small, but high either energy positivity or microcausality is violated some observer frame. However, this can be avoided sub-Planck limit nonlocal theory with spontaneous Our analysis supports...

The behavior of photons in the presence Lorentz and $CPT$ violation is studied. Allowing for operators arbitrary mass dimension, we classify all gauge-invariant Lorentz- $CPT$-violating terms quadratic Lagrange density associated with effective photon propagator. covariant dispersion relation obtained, conditions birefringence are discussed. We provide a complete characterization coefficients dimensions via decomposition using spin-weighted spherical harmonics. resulting nine independent...

We investigate gravitational phenomenology in compactified higher-dimensional theories, with particular emphasis on the consequences string theory of tensor-induced spontaneous Lorentz-symmetry breaking. The role played by this mechanism causing a version Higgs effect and compactification is explored. experimental viability theories zero modes considered examining nonleading but observable effects. Additional constraints from observed cosmological properties Universe are uncovered. Our...

Spontaneous breaking of CPT is possible in string theory. We show that it can arise at a level within reach experiments meson factories currently being built or designed. For $\phi$, $B$, and $\tau$-charm factories, we discuss the likely experimental signatures provide estimates bounds might be attained these machines.

Infrared, optical, and ultraviolet spectropolarimetry of cosmological sources is used to constrain the pure electromagnetic sector a general Lorentz-violating standard-model extension. The coefficients for Lorentz violation are bounded less than 3 x 10(-32).

In a nonperturbative formulation, radiative corrections arising from Lorentz and CPT violation in the fermion sector induce definite nonzero Chern-Simons addition to electromagnetic action. If instead perturbative formulation is used, an infinite class of theories characterized by value coefficient emerges at quantum level.

The pure-gravity sector of the minimal standard-model extension is studied in limit Riemann spacetime. A method developed to extract modified Einstein field equations small metric fluctuations about Minkowski vacuum, while allowing for dynamics 20 independent coefficients Lorentz violation. linearized effective are solved obtain post-Newtonian metric. corresponding behavior a perfect fluid and applied gravitating many-body system. Illustrative examples methodology provided using bumblebee...

We investigate measurable gravitational and cosmological effects in four dimensions that can arise from the compactification of higher-dimensional theories incorporating gravity. identify nature due to massless scalar components compactified metric modifications dynamics. Current experimental data impose constraints on viability many theories, including Kaluza-Klein, supergravity, string theories. The phenomenological problems be avoided if higher acquire an effective mass. survey some...

The behavior of fermions in the presence Lorentz and $CPT$ violation is studied. Allowing for operators any mass dimension, we classify all Lorentz-violating terms quadratic Lagrange density free fermions. result adapted to obtain effective Hamiltonian describing propagation mixing three flavors left-handed neutrinos involving arbitrary dimension. A characterization neutrino coefficients provided via a decomposition using spin-weighted spherical harmonics. restriction general theory various...

The theoretical description of fermions in the presence Lorentz and $CPT$ violation is developed. We classify all Lorentz- $CPT$-violating invariant terms quadratic Lagrange density for a Dirac fermion, including operators arbitrary mass dimension. exact dispersion relation obtained closed compact form, projection spinors are derived. Pauli Hamiltonians particles antiparticles extracted, observable combinations identified. characterize enumerate coefficients any operator dimension via...

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

Constraints from clock-comparison experiments on violations of Lorentz and CPT symmetry are investigated in the context a general Lorentz-violating extension standard model. The experimental signals shown to depend atomic ionic species used as clocks. Certain usually regarded establishing comparable bounds this sensitive different types violation. Some considerations relevant possible future measurements presented. All these potentially physics at Planck scale.

Signals for $\mathrm{CPT}$ and Lorentz violation at the Planck scale may arise in hydrogen antihydrogen spectroscopy. We show that certain $1S\ensuremath{-}2S$ hyperfine transitions can exhibit theoretically detectable effects unsuppressed by any power of fine-structure constant.

A general formalism is presented for violations of Lorentz and CPT symmetry in the neutrino sector. The effective Hamiltonian propagation presence violation derived, its properties are studied. Possible definitive signals existing future neutrino-oscillation experiments discussed. Among predictions direction-dependent effects, including neutrino-antineutrino mixing, sidereal annual variations, compass asymmetries. Other consequences involve unconventional energy dependences oscillation...

A search for sidereal variations in the frequency difference between co-located 129Xe and 3He Zeeman masers sets most stringent limit to date on leading-order Lorentz CPT violation involving neutron, consistent with no effect at level of 10(-31) GeV.

A theoretical analysis is performed of Penning-trap experiments testing CPT and Lorentz symmetry through measurements anomalous magnetic moments charge-to-mass ratios. Possible violations arising from spontaneous breaking at a fundamental level are treated in the context general extension SU(3) x SU(2) U(1) standard model its restriction to quantum electrodynamics. We describe signals that might appear principle, introduce suitable figures merit, estimate bounds attainable present future...

We show that the general Lorentz- and CPT-violating extension of quantum electrodynamics is one-loop renormalizable. The Lorentz-violating beta functions are obtained, running coefficients for Lorentz $\mathrm{CPT}$ violation determined. Some implications theory experiment discussed.

Exceptional sensitivity to spacetime torsion can be achieved by searching for its couplings fermions. Recent experimental searches Lorentz violation are exploited extract new constraints involving 19 of the 24 independent components down levels order ${10}^{\ensuremath{-}31}\text{ }\text{ }\mathrm{GeV}$.

Precision experiments with muons are sensitive to Planck-scale $\mathrm{CPT}$ and Lorentz violation that is undetectable in other tests. Existing data on the muonium ground-state hyperfine structure muon anomalous magnetic moment could be analyzed provide dimensionless figures of merit for at levels $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ ${10}^{\ensuremath{-}23}$.