Classical Particle Models  

Non-Relativistic > s.a. classical systems; mass; particle models; spinning particles.
* Action: Of the form

S[xi; t1, t2] = 12 dt [ m i (x·i)2– V(xi)] .

@ Various backgrounds: Baleanu & Güler JPA(01)ht [in curved spacetime, Hamilton-Jacobi]; Chavchanidze & Tskipuri mp/01 [SU(2) group]; Marques & Bezerra CQG(02)gq/01 [cosmic string].
@ Symmetries: Haas & Goedert JPA(99)mp/02 [2D, Noether]; Jahn & Sreedhar AJP(01)mp [invariance group].
@ Related topics: Fuenmayor et al PRD(02)ht/01 [loop representation, with gauge theory]; van Holten phy/01 [dual fluid interpretation].
@ Variations: Barbour CQG(03)gq/02 [relational dynamics]; > s.a. parametrized theories.

Relativistic Particles > s.a. self-force; test-body orbits.
$ Action, reparametrization-invariant: Two versions, which give the trajectory only as a locus of points, are

S[x] = m0c ds |gab x·a x·b|1/2 = dt (pa x·a – g p2)   or   S[x] =  dt (u–1 gab x·a x·b – um2) ;

The first one (Jacobi-type) is proportional to the length of the world-line, the g(t) is a 1D metric/Lagrange multiplier, like 1D gravity with scalars, and u(t) is an additional variable.
$ Action, proper-time-gauge:

S[x] = m0 dt gab x·a x·b .

* Equation of motion: If a particle is coupled to a field, its equation of motion is just the expression of momentum exchange between particle and field, so it can be obtained from a Ttotab = 0; For a scalar particle in electromagnetic field and linearized gravity, respectively,

dpm/d = q Fmn un = (q/m) Fmn pn ,   dpm/d = (/2) m hab,m uaub .

* Issue: The descriptions using t and the proper time are not equivalent [@ Kalman PR(61); Sonego PRA(91)].
* Issue: If a point particle is included among the field sources, the treatment cannot be made fully consistent.
@ Lagrangian formulation: Potgieter AJP(83), comment Berger AJP(84); Desloge & Eriksen AJP(85).
@ In curved spacetime: Modanese JMP(92) [fluctuating gravitational field]; Piechocki CQG(03)gq/02 [dS, different topologies]; Bini et al CQG(03)gq/02 [in gravitational wave collision]; Barrabès & Hogan CQG(04)gq/03 [deflection]; Chicone & Mashhoon CQG(05)gq/04 [in Fermi coordinates]; Fukumoto et al PTP(06)gq [finite-size, fast-moving]; Ling et al gq/06 [in rainbow spacetime]; > s.a. kerr-newman, scattering.
@ Interacting: Bergmann & Komar GRG(82); Tretyak & Nazarenko CondMP(00)ht; Damour et al PLB(01)gq [3PN]; Lompay ht/05.
@ Stochastic medium: Johnson & Hu PRD(02) [modified Abraham-Lorentz-Dirac equation in a quantum field]; Cabo-Bizet & Cabo Montes de Oca PLA(06).
@ Related topics: Balachandran et al JMP(84) [geometry]; Gill et al IJTP(93), IJTP(98) [proper time formulation]; Horwitz ht/98 [Lorentz force equation from Stückelberg mechanics]; Parrott gq/02 [Rohrlich equation]; Barros et al CQG(05) [with rigidity and torsion]; Uggerhøj RMP(05) [in strong crystalline fields]; Freidel et al PRD(07) [Dirac observables and effective noncommutative geometry].
> Other topics: see mass; non-commutative physics; radiation; scalar field theories; specific heat; statistical mechanics; Test Body.

Variations and Generalizations > s.a. dissipative system; quantum particles [including superparticle]; spinning particles.
$ Charged particle: The length-of-worldline action becomes

S[x] = ds [m0c |gab x·a x·b|1/2 + q Aa x·a] .

* Modified Lagrangian: It can depend on the curvature of the worldline (rigidity) and its torsion.
@ Charged particle: Hyman AJP(97), Muñoz AJP(97) [with constant fields]; Aldaya et al JPA(02) [group cohomology]; Cardoso et al PRD(03) [in Schwarzschild]; Carvalho et al IJMPA(04)gq [with defect distribution]; Timoumi RPMP(04) [closed trajectories]; Lidsky TMP(05) [radiating]; Rohrlich 07; > s.a. self-force [including preacceleration]; Marmo & Tulczyjew RPMP(06) [Poincaré-covariant, and T reflection]; > s.a. electromagnetism.
@ Alternative dynamics: Arreaga et al CQG(01)ht [Frenet-Serrat curvature action]; Pavón JMP(01)qp [stochastic dynamics].

Coupled to Gravity > s.a. 3D gravity; multipoles [extended objects]; orbits; quantum particles; radiation; spinning particles; Test Body.
@ Non-spinning: Kaniel & Itin gq/01; Blanchet & Faye JMP(01)gq/00 [regularization].
@ Charged: Rosen AP(62) [field of particle in motion]; Khriplovich & Pomeransky gq/98-in; Khriplovich ht/00-in [spinning]; Das et al mp/05 [review]; Gorbatenko TMP(05) [Einstein-Infeld-Hoffmann, order (v/c)3].
@ With torsion: Fiziev & Kleinert gq/96 [action]; Kleinert & Pelster GRG(99)gq/96 [autoparallels]; Barros e Sá gq/97; Geyer et al IJMPA(00)ht/99; Pezzaglia gq/99/IJTP; Arroyo et al GRG(04)ht/03; Barros et al IJMPA(04).

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