Non-Commutative Theories in Physics  

In General > s.a. [non-commutative geometry]; lagrangian systems; quantum spacetime; symmetry breaking.
* Motivation: The motivation can be traced to the quantum gravity idea that space(time) points become fuzzed out at the smallest scales, and the fact that one can regularize gauge theories by making the underlying manifold fuzzy; Finite-dimensional systems and quantum mechanics are simpler than field theory and provide useful toy models.
* Remark: They are non-local, and can be considered examples of infinite-order Lagrangian theories.
@ Intros and general references: Chamseddine in(95); Dimakis & Müller-Hoissen phy/97 [intro]; Bigatti CQG(00)ht [intro]; Castellani CQG(00)ht-in [rev]; Schucker ht/01-in, ht/01-in [forces]; Kauffman NJP(04)qp [origin of gauge theory, quantum mechanics]; Rosenbaum et al ht/06/CM, JPA(07) [from symplectic structure and Dirac procedure]; Balachandran et al 07.
@ Relativistic particles: Deriglazov ht/02, PLB(03)ht/02; Malik IJMPA(07)ht/05 [in electromagnetic field, symmetries]; Wohlgenannt ht/06-in [intro]; Balachandran et al JHEP(07)ht [discrete time and energy non-conservation]; > s.a. quantum particles.
@ Spinors: Grimstrup et al EPJC(02)ht/01; Paschke & Sitarz LMP(06) [Dirac operators on non-commutative T2].
@ Spectral action: Chamseddine & Connes CMP(97)ht/96 [proposal]; Besnard JGP(07) [canonical quantization, example]; > s.a. non-commutative geometry.
@ Hamiltonian formalism: Kalau JGP(96); Hawkins CMP(97)gq/96; Lukierski ht/98-in [deformed phase space]; Gomis et al PRD(01)ht/00 [and path integral]; Giunashvili mp/02 [and phase space]; Malik MPLA(03) [and Lagrangian]; Li et al MPLA(05)ht/04 [oscillator with non-commutative phase space]; Cortese & García PLA(06) [eom and symplectic form]; Cuesta et al ht/06 [gauge theories with non-commutative phase space]; Cortese & García ht/07/IGJMP [variational formulation]; Li & Dulat a0708 [nc phase space and spacetime symmetries].
@ Related topics: Gruppuso JPA(05) [classical mechanics]; Kochan ht/06 [classical Lagrangian mechanics]; Pinzul & Stern a0705 [gauging the star product].

Quantum Mechanics > s.a. deformation quantization; path integrals and specific theories.
* Quantization: 1995, One does not know how to quantize non-commutative models directly, but each one can be rewritten as an equivalent field theory in the ordinary sense, which can be quantized.
* And quantum mechanics: A deformed Heisenberg algebra gives rise to discrete position and momentum spectra, → lattice structure.
@ General references: Madore PLB(91), AP(92); Dimakis & Müller-Hoissen JPA(92) [non-commutative symplectic geometry]; Vilela Mendes PLA(96); Adler ht/96-in; Heller & Sasin gq/98, gq/99; Rovelli PRL(99)gq; Wess mp/99-in [Heisenberg algebra]; Nair & Polychronakos PLB(01)ht/00; Acatrinei JHEP(01) [path integral]; Espinosa & Gaete ht/02 [choice of H]; Barbosa & Pinto PRD(04)ht/03 [Bohmian]; Djemai & Smail CTP(04)ht/03; Girotti AJP(04); Riccardi JPA(06)ht/05 [observables]; Muthukumar JHEP(07)ht/06; Bastos et al ht/06 [phase space formulation]; Dulat & Li MPLA(06) [commutator anomaly]; Bemfica & Girotti a0709; Giri a0802.
@ Quantum mechanics in non-commutative spacetime: Balachandran et al JHEP(04)ht [Moyal plane], JHEP(04)ht [cylinder]; Vaquera-Araujo & Lucio mp/05 [plane]; Calmet & Selvaggi PRD(06)ht; Wachter qp/07, qp/07, qp/07.
@ Different C: Morariu & Polychronakos NPB(01)ht [on torus]; Deriglazov PLB(02)ht [on S2].
@ Related topics: Dulat & Li a0802 [Landau problem].
> Related topics: see coherent states; crystals [particle in quasicrystal]; dissipation; scattering; time in quantum theory.

Other Theories and Topics > s.a. Burgers Equation; field theories; fluids; random processes; velocity.
@ Astrophysics / cosmology: Tamaki et al PRD(02)gq/01 [-rays and uhe cosmic rays]; Romero & Vergara MPLA(03)ht [solar system]; Fukuma et al NPB(04) [cmb spectrum]; Pimentel & Mora GRG(05) [quantum cosmology]; > s.a. inflationary phenomenology, non-commutative gravity.
@ Integrable systems: Hamanaka & Toda PLA(03); Giachetta et al PLA(07)qp/06 [quantization].
@ Harmonic oscillators: Hatzinikitas & Smyrnakis JMP(02); Parmeggiani CMP(08) [spectrum, semiclassical].
@ Other systems: Chaichian et al EPJC(04)ht/02 [H atom].
@ Other phenomenology: Acatrinei MPLA(05)ht/03 [experimental effect]; Kauffman qp/03 [discrete physics]; Calmet EPJC(05)hp/04 [bounds]; Balachandran et al PRD(06)ht/05 [waves]; Colatto et al PRD(06)ht/05 [spin effects]; Abel et al JHEP(06) [vacuum birefringence].
> Related topics: see lorentz symmetry modifications, symplectic structures [non-commutative ]; uncertainty.

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