Spinning-Particle Models  

Non-Relativistic, Classical Spinning Particles > s.a. classical particles / classical systems.
@ References: Thomas Nat(26)apr; Bruce qp/01 [spin-1/2, Hamiltonian]; Rivas JUMS-phy/01-in [generalized Lagrangian], JPA(03)phy/01 [spinning electron]; Salesi IJMPA(05)qp/04 [and Zitterbewegung]; Recami & Salesi FP(07)qp/05 [from arbitrary-order Lagrangians, and chronons]; Banerjee & Mukherjee CQG-a2003 [canonical formulation].

Relativistic, Classical Spinning Particles > s.a. particle models / chaotic motion; dirac fields; Thomas Precession; twistors.
* 1998: The motion of spinning particles in gravitational fields is still not well understood; Look for clarification in gravitomagnetism.
* Mathisson-Papapetrou-Dixon equations: For a particle of velocity va, momentum pa, and spin tensor S ab, in the monopole-dipole approximation they are

dua/dτ = va ,    \(Dp^a/D\tau = {1\over2}\)Rabcd vb S cd ,    DS ab/ = pa vbpb va ;

In general, va and pa are not parallel, and one must use an additional condition to fix pa, for example pb S ab = 0.
@ Mathisson-Papapetrou-Dixon equations: Mathisson ZP(31) + tr GRG(10), ZP(37) + tr GRG(10); Papapetrou PRS(51), PRS(51); Dixon PRS(70); Lompay gq/05; Singh GRG(08)-a0706 [perturbation method]; Costa et al PRD(18)-a1712 [momentum-velocity relation]; > s.a. gravitating matter; Wikipedia page.
@ General references: Salesi & Recami AACA-ht/96; Lyakhovich et al NPB(99)ht/98 [any D, integer s]; Niederle & Nikitin PRD(01) [half-integer spin]; Machin ht/01 [1D, with supersymmetry]; Rivas JPA(03)phy/01 [spinning electron]; Salesi IJMPA(02); Rivas JPA(06)ht/05-conf [s = 1/2, symmetry group]; Pol'shin MPLA(09) [variational principle]; Kudryashova & Obukhov PLA(10) [explicitly covariant dynamics]; Bratek JPCS(12)-a1111 [indeterminate worldlines]; Kiriushcheva et al CJP(13)-a1305 [gauge symmetries]; Kaparulin & Lyakhovich PRD(17)-a1708 [massive, flat spacetime world sheets]; Plyatsko & Fenyk a1905 [in a gravitational field]; Obukhov JPCS(20)-a1912 [in external fields, formalism].
@ Lagrangian / Hamiltonian formulations: Muslih mp/00 [canonical]; Bérard et al ht/03 [covariant H]; Hajihashemi & Shirzad IJMPA(16)-a1501; Andrzejewski et al a2008 [coadjoint orbits method].
@ Models: Rębilas AJP(11)oct [Bargmann-Michel-Telegdi theory]; Deriglazov AP(12)-a1107 [classical Dirac particles without Grassmann variables], PLA(12)-a1203 [without observable trajectories]; Rempel & Freidel PRD(17)-a1609 [bilocal model in terms of two entangled constituents], a1612 [in dual phase space]; Kaparulin et al JPCS(19)-a1907 [massive, in 4D Minkowski space].
@ 3D, in 2+1 dimensions: Ghosh PLB(94) [in 2+1 dimensions]; Valverde & Pazetti JHEP(06)ht [massless, supersymmetric variant]; Schuster & Toro PLB(15)-a1404 [massless, with non-trivial physical spin].
@ In curved spacetime: Burman IJTP(77) [worldlines as geodesics of modified connection]; Khriplovich & Pomeransky JETP(98)gq/97 [equations of motion]; Erler gq/99-proc; Pezzaglia gq/99/IJTP-conf [and Clifford algebra]; Turakulov & Safonova MPLA(03)gq/01 [vector]; Chicone et al PLA(05)gq; Wu CTP(08)gq/06 [gravitomagnetism and non-geodesic motion]; Blanchet CQG(07)gq/06 [dipolar particle]; Cianfrani & Montani NCB(07)gq-proc; Khriplovich APPBS(08)-a0801; Mohseni IJTP(08)-a0710 [Lagrangian]; Muminov a0802, a0805 [massless spin-1/2]; Singh & Mobed PRD(09)-a0807, GRG(10)-a0903-GRF [Lorentz-invariance breaking and muon decay]; Costa et al AIP(12)-a1206 [Mathisson's helical motions], PRD(16)-a1207 [gravito-electromagnetic analogies]; Mashhoon & Obukhov PRD(13) [spin precession in inertial and gravitational fields]; d'Ambrosi et al PRD(16)-a1511 [and charged, motion]; Kumar a1512-MG14; Batista & Barbosa dos Santos a2004 [re conserved quantities]; Marsot a2103-PhD.
@ In curved spacetime, Hamiltonian: Barausse et al PRD(09)-a0907; d'Ambrosi et al PLB(15)-a1501; Kunst et al PRD(16)-a1506 [for different tetrad fields]; Witzany et al CQG(19)-a1808.
@ Infinite-spin: Edgren et al JHEP(05)ht, Edgren & Marnelius JHEP(06) [higher-order Lagrangian].
@ Other special types and generalizations: Krishna et al IJMPA(13)-a1210 [1D supersymmetric, BRST formalism]; Deguchi et al IJMPA(14)-a1309 [4D massless, twistor model, canonical]; Buchbinder et al JHEP(18)-a1805 [with continuous spin].
> Related topics: see diffusion; spin, 2-spinors and 4-spinors; spinors in field theory; test-body motion / quantum particles.

Specific Spacetimes and Generalizations > s.a. particles in kerr, reissner-nordström and schwarzschild spacetimes.
@ de Sitter spacetime: Obukhov & Puetzfeld PRD(11)-a1010, a1201-conf; Fröb & Verdaguer JCAP(17)-a1701 [quantum corrections].
@ Schwarzschild-de Sitter spacetime: Ali IJTP(02); Mortazavimanesh & Mohseni GRG(09)-a0904; Plyatsko et al GRG(18)-a1811 [non-equatorial circular orbits].
@ Other black holes: Stuchlik & Kovar CQG(06)gq [Kerr-de Sitter]; Kubizňák & Cariglia PRL(12)-a1110 [higher-dimensional spinning, integrability]; Witzany PRD(19)-a1903 [near black holes, Hamilton-Jacobi equation].
@ Vaidya spacetime: Singh PRD(05); Singh PRD(08)-a0808 [perturbation approach].
@ In other curved spacetimes: Garcia de Andrade gq/02 [Gödel spacetime]; Mohseni PLA(02)gq, et al CQG(01)gq/03 [gravitational wave]; Mohseni IJMPD(06)gq/05 [pp-wave and uniform B field]; Bini et al IJMPD(06)gq [massless, in vacuum algebraically special spacetime]; Obukhov et al PRD(09)-a0907 [in the field of a rotating source]; Barbot & Meusburger GD-a1108 [stationary flat spacetimes]; Zalaquett et al CQG(14)-a1308 [in conformally flat spacetimes]; Toshmatov et al EPJC(20)-a2003 [non-asymptotically flat spacetimes]; > s.a. orbits of gravitating objects [spin-orbit and spin-spin effects].
@ With electromagnetic field: Bargmann et al PRL(59) [precession]; Künzle JMP(72) [and gravitational field]; Cianfrani et al gq/06-MGXI, Cianfrani et al PLA(07) [from 5D Kaluza-Klein framework]; Pozdeeva JSI(09)-a0708 [neutral massive spin-1/2 particle, interaction H]; Barducci et al EPJC(10)-a1006 [with anomalous magnetic moment]; Deriglazov PLA(12)-a1106 [and Zitterbewegung]; Hushwater AJP(14)jan + a1410 [discovery of the classical equations of motion]; Deriglazov & Guzmán AMP(17)-a1710 [in external gravitational and electromagnetic fields]; Obukhov et al PRD(17)-a1708.
@ With torsion: Wanas ASS(97)gq/99 [torsion correction to geodesic]; Messios IJTP(07); Popławski PLB(10)-a0910 [classical Dirac particles cannot be pointlike], a1304 [intrinsic spin requires gravity with torsion and curvature].
@ In non-commutative geometry: Das & Ghosh PRD(09)-a0907 [Hamiltonian]; Dvoeglazov AIP(09)-a0909; Adorno et al PRD(10)-a1008 [wave equation].

Classical Spinning Particles Coupled to Gravity > s.a. classical particles; motion of gravitating bodies.
@ General references: Wald PRD(72); Kánnár GRG(94) [Lagrangian]; Rietdijk TMP(94); Mashhoon APPS-a0801-conf; Cianfrani & Montani EPL(08)-a0810 [Papapetrou coupling from Dirac equation]; Obukhov & Puetzfeld a1509-proc [conservation laws and covariant equations of motion, with minimal and non-minimal coupling]; Fröb JHEP(16)-a1607 [quantum gravitational corrections]; > s.a. tests of the equivalence principle.
@ With electromagnetic fields: Lyakhovich et al IJMPA(00)ht [massive]; Tucker PRS(04).

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