Doubly or Deformed Special Relativity  

In General > s.a. 3D gravity; 4-spinors; non-commutative field theory and geometry.
* Idea: "Doubly special relativity" or "deformed special relativity" (DSR either way) is any theory containing two fundamental, invariant scales–the speed of light and an energy, usually taken to be Ep; The speed of light becomes energy-dependent, with preferred frames avoided by postulating a non-linear representation of the Lorentz group in momentum space.
* Features: Deformed composition laws for energy and momentum, related to spacetime non-locality.
* Status: 2006, The conceptual status is not clear, as the interpretation of a theory in which conserved quantities are not additive is problematic; It is sometimes seen not as a fundamental theory, but as a feature of the low-energy limit of quantum gravity.
@ Intros, reviews: Amelino-Camelia IJMPD(02)gq; Kowalski-Glikman LNP(05)ht/04, in(09)gq/06; Amelino-Camelia Sym(10)-a1003.
@ General references: Amelino-Camelia IJMPD(02)gq/00; Kowalski-Glikman PLA(01)ht; Amelino-Camelia AIP(01)gq; Magueijo & Smolin PRL(02)ht/01, PRD(03)gq/02; Amelino-Camelia Nat(02)gq, et al CQG(03); Judes & Visser PRD(03)gq/02 [conservation laws]; Granik ht/02; Rembieliński & Smoliński Lodz(03)ht/02 [difficulties]; Schützhold & Unruh JETPL(03)gq [problems with variable c]; Liberati et al PRD(05)gq/04 [from measurement phenomenology]; Girelli & Livine gq/04, BJP(05)gq/04-proc [interpretation]; Girelli & Livine JPCS(07)gq/06 [and gravitational constant]; Rovelli a0808 [physical interpretation]; Mignemi PLB(09)-a0808, a1010-MG12 [new interpretation]; Gibbons & Gielen CQG(09)-a0902 [and torsion]; Borowiec & Pachoł JPA(10)-a0903 [classical basis for κ-Poincaré algebra]; Girelli & Livine PRD(10) [lessons from deformed Galilean relativity]; Borowiec & Pachoł Sigma(10)-a1005 [Hopf-algebraic approach]; Relancio a2008-PhD.
@ And other theories, approaches: Calisto & Leiva IJMPD(07)ht/05 [generalized commutation relations]; Girelli et al PRD(10)-a0903 [group field theory]; Calmet et al PRD(10)-a1008 [from asymptotically safe gravity]; Rizzuti & Vasconcelos a2102 [from 5D SO(1,4) action].
@ DSR = special relativity? Ahluwalia gq/02, CQG(05); Jafari & Shariati AIP(06)gq.
@ Velocity: Kosiński & Maślanka PRD(03)ht/02; Mignemi PLA(03); Aloisio et al PRD(04); Daszkiewicz et al PLA(04)ht/03.
@ Other kinematics: Kowalski-Glikman PLB(02)ht [pa-space = 4D de Sitter], ht/02-proc, and Nowak CQG(03); Lukierski & Nowicki IJMPA(03) [and κ-deformation]; Mignemi IJMPD(06)gq/04 [spacetime symmetries]; Dutta & Bhattacharya a1105 [length contraction]; > s.a. deformed minkowski space.
@ In position space: Kimberly et al PRD(04)gq/03; Deriglazov PLB(04)ht; Deriglazov & Rizzuti PRD(05)ht/04; Aloisio et al PLB(05)gq; Hossenfelder PLB(07)gq/06; Mignemi a0711 [from 5D], AdP(10)-a0802 [in de Sitter space].
> Related topics: see examples of lie groups [projective actions of orthogonal groups]; lorentz group [non-linear representations]; supergravity.

Topics and Phenomenology > s.a. deformed minkowski space; modified uncertainty relations; tests of lorentz invariance.
* Phenomenology: The most obvious consequence is a modification of the usual conservation laws; The usual quadratic dispersion relations are modified, so that the speed of light becomes energy dependent (without the presence of preferred frames).
* In cosmology: The theory may be used to induce a varying speed of sound capable of generating (near) scale-invariant density fluctuations.
@ Canonical, phase space version: Błaut et al PLB(04)ht/03; Hinterleitner PRD(05)gq/04; Galán & Mena IJMPD(07)gq [relating frameworks]; Ghosh & Pal PRD(07)ht.
@ And quantum-gravity phenomenology: Kowalski-Glikman ht/03-MGX; Amelino-Camelia et al IJMPA(05)gq/03; Amelino-Camelia gq/04-MGX, IJMPD(05)gq; Smolin NPB(06)ht/05; Imilkowska & Kowalski-Glikman LNP(06)gq/05; Aloisio et al PRD(06)gq/05 [DSR as effective measurement theory], PRD(06)gq [quantum gravity fluctuations]; > s.a. semiclassical quantum gravity.
@ Particles and fields: Ahluwalia-Khalilova gq/02-proc, IJMPD(04) [fermions & bosons]; Girelli et al PRD(06)ht/05 [free particle]; Heuson gq/06 [field quantization]; Ghosh PRD(06), comment García PRD(07)-a0704 [particle dynamics and non-commutativity]; Hossenfelder PRD(07)ht [multi-particle states]; Hinterleitner CQG(08)-a0706 [low-energy limit not Newtonian gravity]; Mandanici MPLA(09)-a0707 [version with additive energies]; Mignemi PLA(09) [lifetime of unstable particles]; Belhadi et al IJMPA(12)-a1106 [Dirac equation]; Chung et al PhyA(19)-a1808 [photons].
@ Non-locality: Hossenfelder a0912 [bounds on deformations from "box problem"]; Hossenfelder a1005, a1006.
@ Light propagation: Błaut et al MPLA(03)ht [with light cone deformation]; Kim et al JKPS(04)gq.
@ Non-relativistic limit: Coraddu & Mignemi EPL(10)-a0911 [and particle masses]; Jafari & PourNemati a1104 [and modified Klein-Gordon and Dirac equations].
@ Other topics: Livine & Oriti JHEP(05) [3D, coherent states]; Hackett CQG(06) [asymptotic flatness]; Magueijo CQG(08)-a0807 [and cosmology]; Rizzuti & Deriglazov PLB(11)-a1106 [from 5D mechanics].
> Related topics: see ideal gas; thermodynamic systems [photon gas]; types of gauge theories; types of quantum field theories.

Generalizations, Other Proposals > s.a. Gravity's Rainbow; modified lorentz symmetry [very special relativity]; poincaré group / algebra.
@ General references: Ballesteros et al JPA(03)ht [from quantum Weyl-Poincaré algebra]; Nassif Pra(08)-a0711 [with a minimum speed]; Magpantay PRD(11) [dual DSR]; Carmona et al Symm(19)-a1911 [modified spacetime and effects]; > s.a. modified general relativity.
@ And Finsler geometry: Mignemi PRD(07)-a0704; Dhasmana & Silagadze MPLA(20)-a1911 [deformation of ISIM(2)].
@ Triply special: Kowalski-Glikman & Smolin PRD(04)ht; Chrissomalakos & Okon IJMPD(04) [Lie-algebra form].

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