Particles: Geometrical Models  

In General > s.a. electron; general relativity solutions; quantum-gravity phenomenology; spinning particles.
* Early developments: In the 1940s Einstein tried unsuccessfully to model particles with regular solutions of the vacuum field equations (including in Kaluza-Klein theory with Pauli) and published negative results.
* As defects / singularities: For example, punctures in 3D gravity (whose geometry is that of conical singularities in an otherwise flat space and are classified by conjugacy classes in the symmetry group G, holonomies modulo gauge transformations, labeled by m and s), or Louis Crane's idea based on simplicial complexes and state sum models.
* Charged particles: Models usually require negative mass in order to maintain stability against Coulomb's repulsion, e.g., a core of negative mass surrounded by a positive-mass, Reissner-Nordström outer layer.
* Spinning particles: In special relativity a particle with spin must always have a finite extension [@ in O'Connell JPA(16)-a1603].
@ General references: Einstein RUNT(41); Damour in(83); Lopez PRD(88); Mann & Morris PLA(93)gq; Kuzenko et al IJMPA(95) [arbitrary spin]; Recami et al gq/95; Vigier PLA(97) [extended, charged]; Zloshchastiev CQG(99)gq/97 [charged]; Galvagno & Giribet EJP(05)phy/04 [Einstein 1941]; Hadley phy/06-talk; Feoli IJMPD(07) [solution of linearized Einstein equation]; Atiyah et al PRS(12)-a1108 [Riemannian 4-manifolds with self-dual Weyl tensor].
@ Semiclassical: Delaney IJTP(73), IJTP(74); Puthoff IJTP(07) [electron and Casimir vacuum energy]; Duval & Horváthy PRD(15)-a1406 [chiral fermion model with a "Berry term", symplectic framework]; > s.a. orbits of gravitating objects.
@ Higher-dimensional: Einstein & Pauli AM(43) [Kaluza-Klein]; Balasubramanian & Larsen NPB(97) [as extremal branes]; Dubois-Violette NPB(16)-a1604 [exceptional real Jordan algebra of dimension 27 and internal particle geometry].
@ Emergent particles: Levin & Wen PRB(05), RMP(05)cm/04 [photons and electrons as string-net condensation, and tensor category theory]; > s.a. 2-spinors [Weyl excitations in solids]; pilot-wave theory [relativistic].
> Related topics: see composite quantum systems; Elementarity.

As Point Particles
@ In general relativity: Blanchet & Faye JMP(01)gq/00; Fiziev gq/04-proc; Casadio et al PLB(09) [and gup]; Tahvildar-Zadeh RVMP(11)-a1012 [electrovacuum spacetimes with mild singularities]; Katanaev GRG(13)-a1207; Benjamin & Allen GRG(18) [and self-interaction].
@ In other theories: van Holten NPB(98)ht/97 [interacting with scalar and vector fields, stability and mass]; Bratek JPA(11)-a1006 [fundamental relativistic rotor]; Kryukov JPCS(13)-a1302 [as Dirac delta functions].

As Field Configurations > s.a. particle types / dirac fields; field theory; hadrons [model for quarks]; non-linear electromagnetism; solitons.
@ General references: Nambu IJTP(78) [stringlike configurations in Weinberg-Salam theory]; Barut & Grant FPL(90), Barut & Bracken FP(92) [free electromagnetic field]; Avelar et al PLA(09)-a0906 [lumplike structures in scalar-field models]; Popławski PLB(10) [Dirac field in Einstein-Cartan-Kibble-Sciama theory]; Fisher & Oliynyk CMP(12)-a1104 [(no) magnetically charged particle-like solutions]; Christov WM(16)-a1203 [solitons].
@ Defects: Duan & Li JMP(98)ht, Li CQG(01)gq/99 [disclinations as particles]; Olkhov AIP(07)-a0801 [Dirac and Maxwell fields as defects]; Kleman a0905; Arzano a1212-FQXi [deformed algebra of creation and annihilation operators].
@ Knots, braids: Bilson-Thompson et al a0804 [quantum geometry excitations]; Bilson-Thompson et al JMP(09)-a0903 [framed braids]; > s.a. knots in physics; strings.
@ Other topological models: Zhuraviev FP(11) [topological interpretation of electric charge]; Asselmeyer-Maluga Symm(19)-a1910 [based on 3-manifolds].
@ Other models: Battey-Pratt & Racey IJTP(80); Freidel et al PRD(06)gq [as Wilson lines]; Casadio et al PLB(09)-a0904 [quasi-pointlike shell, with gup]; Burnell & Simon AP(10)-a1004 [geometrical space-time picture of Levin-Wen models]; Freidel et al PRD-a1812 [metaparticles].

As Black Holes and Related Spacetimes > s.a. born-infeld theory, and electrons above.
* Remark: The issue is that for known particles like the electron in natural units we have q \(\gg\) m, so it seems like they would have naked singularities; One way out (in an approximate approach) is to remember that at very small scales, the electric potential is logarithmic rather than 1/r.
* As wormholes: For example, wormholes can have charge without a source of charge.
@ General references: Holzhey & Wilczek NPB(92); Kim hp/98-proc; Sidharth IJMPA(98)qp; Burinskii CQG(99)ht-conf; Arcos & Pereira GRG(04)ht/02 [Kerr-Newman black hole as Dirac particle]; Burinskii & Hildebrandt G&C(03); Zaslavskii PRD(04)gq [Reissner-Nordström matched to Robinson-Bertotti]; Petrov FPL(05)gq [Schwarzschild]; Goncharov in(05)ht [black holes and confinement]; Oldershaw JCosm(10)ap/07 [hadrons as Kerr-Newman solutions]; Ha IJMPA(09)-a0906-conf; Stoica PS(12)-a1111 [charged particles]; Arkani-Hamed et al a1906 [Kerr black holes].
@ Electrons as Kerr black holes: Burinskii G&C(08)ht/05, CzJP(06)ht/05-conf, gq/06-MG11, a0712-conf; Burinskii JPCS(12)-a1212.
@ As wormholes: Clément gq/98 [ring wormholes].
@ Corrected electromagnetic potential: Kauffmann ht/94; Blinder RPMP(01), RPMP(01)mp; Ward MPLA(04), JCAP(04); Ponce de León GRG(04)gq/03; > s.a. modified electromagnetism.

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