Momentum  

In General, and Particle Mechanics > s.a. hamiltonian dynamics and systems; phase space.
* Idea: The conserved quantity related to spatial translation invariance of a theory (from movimentum).
* In classical non-relativistic mechanics: A particle with velocity v has momentum p = mv.
* In special relativistic mechanics: A particle with 4-velocity ua has 4-momentum pa = mua.
@ General references: Sibelius FP(90) [mechanical and wave-theoretical aspects]; Crenshaw PLA(05) [electromagnetic, and Fresnel relations]; Roche EJP(06) [general definition]; Lee SHPMP(11) [examples of momentum non-conservation in classical mechanics].
@ History: Gillespie AJP(95)apr [why "p"? :-)]; Graney TPT(13)-a1309 [John Buridan's 14th century concept].
@ In special relativity: Sonego & Pin EJP(05), EJP(05); Adkins AJP(08)nov; Riggs TPT(16) [vs Newtonian dynamics].
@ Other systems: Liu et al PRA(11) [free particle on a 2-sphere, geometric momentum]; Exner a1205-fs [on graphs]; Liu JMP(13) [particle on a curved hypersurface].
> Related topics: see conservation laws.

Momentum-Space Geometry > s.a. finsler geometry.
@ General references: Freidel & Smolin a1103 [and photon propagation]; Amelino-Camelia et al CQG(12)-a1107 [distant observers and phenomenology]; Kowalski-Glikman IJMPA(13)-a1303 [curved, rev]; Freidel & Rempel a1312 [scalar quantum field theory in curved momentum space]; Freidel et al IJMPD(14)-a1405-GRF [dynamical momentum space and string theory]; Lobo & Palmisano a1612-proc [isometry group and Planck-scale-deformed co-products].
@ Relative locality: Kowalski-Glikman IJGMP(12)-a1205-proc [and curved momentum space]; Amelino-Camelia et al a1307; Banburski & Freidel PRD(14)-a1308 [non-commutativity related to Snyder spacetime]; Amelino-Camelia a1408 [non-linear composition law and the soccer-ball problem]; > s.a. Fermi Surface.
@ Phenomenology of curved momentum space: Amelino-Camelia et al PLB(16)-a1605, a1609 [dual redshift and dual lensing]; > s.a. modified thermodynamics [photon gas in curved momentum space].

In Field Theory
* In general: The momentum density of matter Tab as seen by an observer ta is – tbT ab.
@ For an electromagnetic field: Babson et al AJP(09)sep; Spavieri & Gillies G&C(10)-a1005 [speed of light in moving media, and photon mass]; Brevik & Ellingsen AP(11)-a1008, comment Griffiths AP(12) [in media]; Griffiths AJP(12)jan [RL]; Crenshaw AP(13) [field and matter momentum in a linear dielectric]; Franklin AJP(14)sep [static electromagnetic fields]; Corrêa & Saldanha PRA(16)-a1601 [and reflection by a quantum mirror]; Singal AJP(16)oct; Brevik a1610 [Minkowski momentum].
@ Internal electromagnetic momentum and "hidden" momentum: Boyer AJP(15)may-a1408, PRE(15)-a1408; > s.a. magnetism.
@ For a fluid: Vishwakarma ASS(09)-a0705, Jagannathan AJP(09)may [pressure contribution to fluid momentum density].
> For an electromagnetic field: see energy-momentum tensor [including the Abraham-Minkowski dilemma, for light]; fields in media; maxwell theory.
> For gravity: see canonical general relativity [various formulations]; gravitational energy-momentum.

In Quantum Theory > s.a. quantum field theory in generalized backgrounds; wigner function.
* Quantum mechanics: A momentum operator conjugate to a configuration variable is one with the right commutation relations; If classically the momentum is associated to a vector field ua on configuration space C, a quantum momentum operator can be defined by û ψ(x):= i (£u + \(1\over2\)div u) ψ(x), where the divergence is calculated using the volume element on C with respect to which the operator must be self-adjoint.
* For a wave: A 1-particle wave with wave vector k has momentum p = ℏk, or p = h/λ.
@ Quantum mechanics: Jordan AJP(75)dec; Roy et al RMF-a0706 [in general coordinates]; Gaveau & Schulman JPA(12)-a1206 [relative momentum of identical particles]; Berry EJP(13) [five different, equivalent definitions]; Xiao & Liu a1605 [canonical momentum vs geometric momentum].
@ Radial momentum: Paz EJP(01)qp/00; Mosley mp/03; Liu & Xiao a1411.
@ Non-trivial configuration spaces: Shikano & Hosoya JMP(08) [on a half-line]; Liu et al IJGMP(13)-a1212 [on a 2-sphere, and coherent states].
@ Maximum momentum: Ching & Ng MPLA(14)-a1311 [effect on wave equations]; > s.a. deformation quantization; deformed uncertainty relations.
@ Other systems, quantum field theory: de Haan ht/06 [electron mechanical momentum in QED]; Arzano CQG(14)-a1305 [3D semiclassical gravity with point particles, deformed Fock space]; Oliveira & Saldanha PRA(15)-a1507 [hidden momentum in a hydrogen atom in an external electric field].


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