Magnetic Monopoles  

Abelian / Dirac Monopoles > s.a. QED [flux quantization, curved spacetime].
* History: 1931, First proposed by Dirac; 14 feb 1982, Event with monopole signature in Blas Cabrera's SQUID; 2003, Team from Japan, China and Switzerland claim they have found indirect evidence, based on the anomalous Hall effect; 2007, Still no confirmation.
* Idea: Particles that carry isolated N or S magnetic poles; Solutions of · B = 0, with B not of the form × A; They are characterized by H2(R3 \ {0};R) = H2(S2;R) = R.
* Classification: The gauge group is U(1), so monopoles are classified by U(1)-bundles P over R3 \ {0}, homotopic to S2, i.e. by elements of 1(S1) = Z, the integer n (magnetic charge) being evaluated by calculating the characteristic class c1(P), and integrating it over S2:

C1 = –(1/2) tr S^2 F = n .

* Coupling strength: Since ge/c = n/2, from e2/c = 1/137 we get g2/c = (137/4) n2, an enormous value.
* Particle trajectories: A charged particle will spiral inward to a minimum distance, then outward; There are no bound states.

References > s.a. gravitational collapse; electromagnetism.
@ General: Dirac PRS(31); Schwinger Sci(69)aug; Wu & Yang PRD(75); Yang pr(79); Von Baeyer ThSc(90); Staruszkiewicz in(92)ht/98; Bakker et al PRL(98) [in SU(2) gauge theory ]; Lynden-Bell & Nouri-Zonoz RMP(98)gq/96 [interactions]; Kalogeropoulos IJGMP(04)mp/05 [and differential characters]; Vento ap/05 [signatures].
@ Reviews: Carrigan NC(65); Sandars CP(66); Amaldi in(68); Goldhaber & Trower AJP(90)may-RL; Shnir 05.
@ Particle dynamics: Rodrigues Sobreira & Bezerra de Mello G&C(99)ht/98; Banerjee & Ghosh IJMPA(00); Pitelli & Letelier PRD-a0911 [massive scalar quantum particle].
@ And charge quantization: Dirac PR(48); Jackiw IJMPA(04)ht/02-in; Nesterov & de la Cruz PLA(04)ht, JMP(08)ht/04 [and representations of rotation group]; Leal & López JMP(06)ht/04 [in loop representation].
@ And general relativity / cosmology: Borde et al PRD(99)gq/98 [collisions and baby universes]; Arreaga et al PRD(00)gq [stability].

Non-Abelian Monopoles > s.a. symplectic structures.
* Idea: Classical soliton solutions in gauge theories, with non-abelian (e.g., color) magnetic charge; Most known exact solutions are static.
* In Yang-Mills-Higgs theory: SU(2)-valued pairs (A, ), with A a connection and a scalar field, with energy

E =   d3x [B2 +(D)2 + (2–C2)] ,

where B:= × A + [A, A] and D:= + [A, ]; One way to obtain solutions is to minimize E with the constraint 2 = C2, which gives the Bogomolny Equation, with the BPS solutions.
@ General references: 't Hooft NPB(74); Polyakov JETPL(74); Goddard & Olive RPP(78); Hitchin CMP(82); Díaz & Lázaro-Camí a0811.
@ Books, reviews: Atiyah & Hitchin 88; Murray mp/01; Tyurin RMS(02) [mathematical]; Ritter mp/03; Bais ht/04-in [history]; Konishi LNP-ht/07.
@ And sigma models: Witten PRD(79); Forgács et al PRL(80).
@ Quantization: Auzzi et al NPB(04)ht, Konishi ht/04-in [quantum and topological aspects]; Qandalji IJTP(06)ht/05 [Dirac, axial gauge].
@ Related topics: Bais & Primack NPB(77) [spherical]; Mazur & Richter PLA(85) [uniqueness]; Labastida & Mariño PLB(95)ht [Lagrangian], NPB(95)ht; Houghton JHEP(00)ht/99 [and Legendre transform]; van der Bij & Radu IJMPA(03) [no Yang-Mills-Higgs rotating in Minkowski].

Solutions > s.a. [QCD]; general relativity solutions; gauge theory solutions; instantons; kaluza-klein models; non-commutative field theory; supersymmetry in field theory; topological field theories.
* BPS (Bogomolny-Prasad-Sommerfield): An extreme self-dual, spherically symmetric monopole solution of the Bogomolny equation in gauge theory.
@ General references: Prasad & Sommerfield PRL(75); Sutcliffe IJMPA(97)ht [BPS, rev]; Kovner et al JHEP(02)hl [existence?]; Bielawski CMP(98) [and Gibbons-Manton metric].
@ 't Hooft-Polyakov: Kleihaus et al MPLA(98) [interaction energy]; Lepora PLB(02)ht/01 [embedded in larger G]; Bais & Striet PLB(02)ht [in Alice electrodynamics]; Rajantie JHEP(06) [mass, quantum]; Qandalji JPA(07)ht [restoration of Lorentz invariance].
@ 't Hooft-Polyakov, excited: Fodor & Rácz PRL(04); Forgács & Volkov PRL(04).
@ BPS multimonopoles: Taubes CMP(82); Gibbons & Manton PLB(95)ht; Gibbons & Townsend PLB(95)ht.
@ In Einstein-Yang-Mills: Weinberg ht/99-in; Bjoraker & Hosotani PRD(00)ht; Gibbons & Townsend CQG(06) [higher-dimensional].
@ In Einstein-Yang-Mills-Higgs: Lue & Weinberg PRD(99)ht; Kleihaus & Kunz PRL(00)ht [monopole-antimonopole]; Hartmann et al PRL(01)ht/00; Bronnikov et al JETP(02)gq [gravitational properties]; Brihaye & Ioannidou CQG(05) [SU(5) monopoles]; Oliynyk AHP(06)-a0810 [existence].
@ Supersymmetric: Chamseddine & Volkov PRL(97) [supergravity]; Lü, Pope & Stelle CQG(98)ht/97 [p-brane, supergravity]; Chalmers & Hanany NPB(97) [3D supersymmetric gauge theory]; Stern & Yi PRD(00)ht [supersymmetric dyons]; Rebhan et al JHEP(06) [corrections to mass and charge]; Weinberg & Yi PRP(07)ht/06 [rev].
@ Related topics: Olive CzJP(82) [self-dual]; Goncharov MPLA(98) [SU(n), Kerr]; Baez et al CMP(00)ht/98 [in fuzzy physics]; Li & Lu PRD(00)gq [in Brans-Dicke theory]; Lugo et al PLB(00) [in Anti-de Sitter space]; Meckes ht/02 [SU(5)]; Díaz & Lázaro-Camí a0811 [arbitrary dimension]; Kihara a0910 [5D, multi-charged Tchrakian monopoles].

Phenomenology and Searches > s.a. Bogomolny Inequality; cosmic rays; duality; topological defects; types of black holes.
* Early-universe production: It arises from the spontaneous breaking of a symmetry group G to G/H, when 3(G/H) = 0, so that there can be point defects in the fields.
* Experimental searches: 2009, Evidence that effective (not fundamental) monopoles are found in spin ices, a family of rare-earth compounds.
* Cosmic ray monopole flux limit: f 7.1 × 10–11/cm/sr/sec.
* Mass predictions and limits: In GUTs, about 1016 GeV; Experimentally, mmon 600 GeV if s = 0, 900 GeV if s = 1/2.
@ Early-universe cosmology: & Kibble; Everett, Vachaspati & Vilenkin PRD(85) [annihilation]; Rajantie PRD(03)hp/02 [phase transitions].
@ Experimental searches: Alvarez et al Sci(70)jan [lunar sample]; Cabrera PRL(82) [event]; Incandela et al PRD(86) [flux limit]; Friseh Nat(90)apr; Abbott et al PRL(98) [mass limit]; Kalbfleisch et al PRL(00) [bounds]; Wick et al APP(03)ap/00 [signatures]; Fang et al Sci(03)oct + pw(03)oct [claim]; Lubsandorzhiev NIM-ap/05 [neutrino telescopes, speculative]; Milton RPP(06)he [status]; Matson SA(09)sep [evidence in spin ices].
@ Gravitational effects: Chakraborty PS(98); Rahaman & Ghosh MPLA(08)-a0801 [semiclassical, in Brans-Dicke theory]; Kagramanova et al GRG(08) [orbits].
@ Other topics: Bal & Schechter PRD(84) [and p decay]; Achúcarro et al JHEP(05)ht [decay of deficit angles]; Vento IJMPA(08)-a0709 [monopole-antimonopole bound states]; Pietilä & Möttönen PRL(09) [creation in a spinor BEC]; news BBC(09)oct [effective monopoles in spin ice, and "magnetricity"].

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