Modifications and Violations of Lorentz Symmetry  

In General > s.a. discrete spacetime; Lorentz-symmetry phenomenology.
* Motivations for violation: Could explain the existence of ultra high-energy cosmic rays beyond the GZK cutoff, and the observations of multi-TeV gamma-rays from Mkn 501; Could be associated with a cutoff scale which regularizes quantum field theory and black-hole entropy calculations.
* Mechanisms: Arises naturally in some versions of quantum gravity (but not in lqg!), string theory, and quantum field theory radiative corrections in non-trivial backgrounds, in which either not all inertial frames are equivalent (spacetime discrete structure and fluctuations at Planck scales with an effectively preferred frame), or kinematical Lorentz group transformations from one frame to another are non-linearly deformed ("doubly special relativity''); Can also arise in some semiclassical gravity models in which Minkowski space is unstable and there is a phase transition to dS space.
@ Reviews: González-Mestres phy/00-in [high-energy astrophysics]; Gambini & Pullin gq/01-in [canonical quantum gravity]; Kostelecky hp/01-in [and CPT]; Amelino-Camelia gq/01-in [with l and v scales], gq/02 [lqg and non-commutative geometry], gq/03-in [approaches]; Colladay AIP-hp/03; Lehnert PRD(03)gq [framework]; Bluhm pw(04)mar; Kostelecky SA(04)aug; Jacobson et al gq/04-in, hp/04-in, AP(06)ap/05; Lehnert gq/06-in, a0711/JPA; Iorio JPCS(07)phy/06; Amelino-Camelia et al IJMPA(080-in [at Planck scale]; Liberati & Maccione ARNPS(09)-a0906 [and constraints].
@ Spontaneous breaking: Yokoi PLB(01)ht/00 [2+1]; Colladay hp/01-in; Moffat IJMPD(03) [and cosmic rays]; Jenkins PRD(04)ht/03; Graesser et al PLB(05)ht [in gravitational couplings]; Dvali et al PRD(07)ht [without spacetime geometry effects]; Bluhm a0704-in, et al PRD(08)-a0712, Bluhm PoS-a0801 [Goldstone modes]; > s.a. Goldstone Boson; symmetry breaking.
@ Related topics: Amelino-Camelia PLB(01)ht/00 [minimum L]; Greenberg PRL(02)hp [and CPT]; Barbero & Villaseñor PRD(03)gq [effective actions and Euclidean general relativity]; Collins et al PRL(04)gq [size of effects]; Hinterleitner PRD(05)gq/04 [canonical methods]; Amelino-Camelia ap/04-in [test theories]; Libanov & Rubakov JHEP(05)ht [infrared modification, ghosts-tachyons]; Jacobson & Wall a0804-GRF [emergence required by second law of thermodynamics]; Potting AIP(06)-a0902 [and masslessness of gravitons]; Visser PRD(09) [as quantum field theory regulator]; Hagar SHPMP(09) [conceptual].
> Related topics: see renormalization.

Modifications of the Lorentz Group > s.a. branes; finsler geometry; non-commutative geometry; poincaré group; sound.
* Preferred vector field: A theory with a preferred vector field, or a preferred frame, is sometimes called "Einstein-Ether theory"; A preferred W a can be used to write dispersion relations or field theory Lagrangians

pa pa = gamma(mP)–1 (W a pa)3 ,       = phi(mP)–1 (W a a)3 .

@ Einstein-aether: Jacobson & Mattingly PRD(01)gq/00, PRD(01)gq/00, gq/01-in [in general relativity], PRD(04)gq; Eling et al gq/04-in; Bertolami & Páramos PRD(05)ht [vacuum solutions]; Foster PRD(05); Foster & Jacobson PRD(06) [PN parameters]; Eling & Jacobson CQG(06) [spherical solutions], PRD(06)gq [2D theory]; Garfinkle et al PRD(07)gq [gravitational collapse]; Eling et al PRD(07)-a0705 [neutron stars]; Foster PRD(07)-a0706 [binaries, strong field effects]; Bonvin et al PRD(08) [solar system]; Jacobson a0711-in, PoS-a0801 [rev]; Withers CQG(09)-a0905 [quantum effective field theory]; > s.a. black holes; Ether; gödel solutions.
@ Einstein-aether, cosmology: Tartaglia & Radicella PRD(07); Li et al PRD(08)-a0709 [primordial perturbations]; Zuntz et al PRL(08)-a0808.
@ Maximal acceleration: Nesterenko et al PRD(99) [and regularization]; Lambiase IJTP(01); Papini PLA(02) [stellar stability]; Feoli IJMPD(03)gq/02; Rama MPLA(03)ht/02 [-deformed Poincaré]; Toller ht/03 [geometries]; > s.a. kerr spacetime.
@ Deformations and quantum version: Finkelstein JMP(96), LMP(00)ht [spin-statistics]; Azcárraga et al qa/97 [h-deformation]; Buffenoir & Roche CMP(99)qa/97; Lagraa JGP(00); Lukierski & Nowicki IJMPA(03)ht/02, APPB(02)ht, ht/02-in; Amelino-Camelia et al CQG(04) [-Poincaré algebras, and cosmological constant]; Daszkiewicz et al MPLA(08) [and 4-momentum addition]; > s.a. minkowski space; modified QED [at cosmological scales].
@ Other topics: Bruno et al PLB(01)ht [boosts that saturate]; Lindesay mp/03 [extension].

Modified Action of the Lorentz Group > s.a. poincaré group; doubly special relativity.
@ References: Manida gq/99 [precursor]; Yokoi PLB(01)ht/00 [non-linear]; Toller MPLA(03)ht [transformation of momentum-energy]; Broekaert FP(05)gq/03-in [gravitationally modified]; Tsabary & Censor mp/04.

Models and Theories > s.a. doubly special relativity; interactions; modified electromagnetism; particle physics; QED; modified QED.
@ Lorentz-violating dispersion relations: Bertolami & Rosa PRD(05)hp/04 [cubic]; > s.a. matter phenomenology in quantum gravity.
@ Standard model extensions: Colladay & Kostelecky PRD(98)hp; Kostelecky PRD(04)ht/03 [and gravity]; Alfaro PRL(05)ht/04 [from quantum gravity]; Alfaro AIP(07)-a0704 [maximum velocities]; Bolokhov & Pospelov PRD(08) [dimension-5 Lorentz-violating interactions].
@ Non-commutative: Carroll et al PRL(01)ht; Carmona et al PLB(03)ht/02; Giri & Shreecharan a0812; > s.a. non-commutative geometry.
@ Gravity: Gabadadze & Grisa PLB(05)ht/04 [massive]; Kostelecky & Potting GRG(05)gq, PRD(09)-a0901; Ferrari et al PLB(07)ht/06 [linearized]; Grisa JHEP(08)-a0803 [massive gravity from Lorentz-violating potential term]; Potting JPCS(09)-a0904; Blas et al a0905; Nojiri & Odintsov a0905 [Horava-like covariant theory]; > s.a. horava-lifshitz gravity.
@ Quantum gravity: Alfaro et al PRD(04)gq; Sudarsky & Caicedo JPCS(05); Vucetich gq/05; Alfaro PRD(05)ht [hadron effects including GZK anomaly]; Lehnert IJMPA(05)ap; Collins et al ht/06-in; Jackiw a0709-in [diffeomorphism-invariant]; Moffat a0905; Koslowski & Schenkel a0910 [functional-renormalization-group methods].
@ Analog models: Weinfurtner et al JPCS-gq/05; Liberati et al PRL(06)gq/05 [and naturalness issue].
@ Brane world: Csáki et al GRG(01)gq [and cosmological constant]; Stoica JHEP(02)ht/01; Bekaert et al JHEP(02)ht; Rizzo JHEP(05).
@ String theory: Bertolami CQG(97)gq; Ambjørn et al PRD(02)ht/01 [matrix models]; Mavromatos ht/02-in, PoS-a0708 [non-critical].
@ Very Special Relativity: Cohen & Glashow PRL(06); Gibbons et al PRD(07)-a0708 [and Finsler geometry].
@ Vector field with vev: Cheng et al JHEP(06)ht; Hashimoto JHEP(08) [Kraus-Tomboulis model, properties].
@ Other theories: Colladay & McDonald JMP(02)hp [and spinors]; Kostelecky et al PRD(02)ht/01 [electrodynamics]; Myers & Pospelov PRL(03)hp; Cardone & Mignani 04; Altschul PRD(05)ht/04 [non-locally modified scalar]; Altschul & Kostelecky PLB(05) [non-polynomial vector field theories]; Mariz et al JHEP(05) [effective Chern-Simons at finite T]; Carmona & Cortes ht/06-in [beyond effective field theories]; Mariz et al BJP-ht/06-in [radiative corrections to Chern-Simons-like terms]; Rashidi & Salehi PLB(07); Parentani PoS-a0801 [breaking by UV dissipative effects].
> Other theories: see chern-simons theory; gravitation; interactions [instantaneous]; particle physics; quantum-gravity phenomenology; scalar-tensor theories; quantum spacetime; supergravity; supersymmetric theories; supersymmetry phenomenology.

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