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 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.

@ __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.

@ __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].

@ __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];
Zhuraviev FP(11) [topological interpretation of electric charge].

> __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.

@ __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].

**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].

@ __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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