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 seen in Blas Cabrera's SQUID; 2003, Team from Japan, China and Switzerland claim they have found indirect evidence, based on the anomalous Hall effect; 2010, 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(\(\mathbb R^3\) \ {0};\(\mathbb R\)) = H2(S2;\(\mathbb R\)) = \(\mathbb R\).
* Classification: The gauge group is U(1), so monopoles are classified by U(1)-bundles P over \(\mathbb R\) \ {0}, homotopic to S2, i.e., by elements of π1(S1) = \(\mathbb Z\), the integer n (magnetic charge) being evaluated by calculating the characteristic class c1(P), and integrating it over S2:

C1 = −\(1\over2\pi\)tr S2 F = n .

* Coupling strength: Since ge/\(\hbar\)c = n/2, from e2/\(\hbar\)c = 1/137 we get g2/\(\hbar\)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; solutions and phenomenology.
@ General: Dirac PRS(31); Ramsey PR(58) [and discrete symmetries]; Ferrell & Hopfield Physics(64); Schwinger Sci(69)aug; Wu & Yang PRD(75); Dirac IJTP(78); Yang pr(79); Von Baeyer ThSc(90)jul; 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]; Weinberg 12.
@ History: Bais in(05)ht/04; Aloisi & Nali Ulisse-a1608-RG [Dirac]; news sn(18)jan [brief search update].
@ Reviews: Carrigan NC(65); Sandars CP(66); Amaldi in(68); Goldhaber & Trower AJP(90)may [RL], 91; Shnir 05; Rajantie CP(12)-a1204; Mavromatos & Mitsou IJMPA(20)-a2005.
@ Particle dynamics: Rodrigues Sobreira & Bezerra de Mello G&C(99)ht/98; Banerjee & Ghosh IJMPA(00); Pitelli & Letelier PRD(09)-a0911 [massive scalar quantum particle]; Ushakov IJTP(11)-a1004 [charged particle in the field of a magnetic monopole, phase space]; Vaz IJTP(13) [Clifford algebra approach]; Dimock a2005 [quantum charged particle]; > s.a. quantum particles; spin-1 particles.
@ And charge quantization: Dirac PR(48); Jackiw IJMPA(04)ht/02-conf; Nesterov & de la Cruz PLA(04)ht, JMP(08)ht/04 [and representations of rotation group]; Leal & López JMP(06)ht/04 [in the loop representation]; Goldhaber & Heras a1710 [with non-zero photon mass]; Heras CP(18)-a1810 [rev].
@ And general relativity / cosmology: Gibbons LNP(91)-a1109 [gravitating, and black holes]; Borde et al PRD(99)gq/98 [collisions and baby universes]; Arreaga et al PRD(00)gq [stability]; Marunović & Prokopec PLB(16)-a1411 [global monopoles and topology change].

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, φ), with A a connection and φ a scalar field, with energy

E = \(1\over2\) d3x [B2 + ()2 + λ(φ2C2)] ,

where B:= ∇ × A + [A, A] and := ∇φ + [A, φ]; One way to obtain solutions is to minimize E with the constraint φ2 = C2, which gives the Bogomolny Equation, with the BPS solutions.
@ General references: 't Hooft NPB(74); Polyakov JETPL(74); Goddard & Olive RPP(78); Freund IJTP(78); Hitchin CMP(82); Díaz & Lázaro-Camí a0811; Evslin JHEP(18)-a1801 [spiked, with two charged scalar Higgs fields].
@ Books, reviews: Marciano IJTP(78); Atiyah & Hitchin 88; Murray mp/01; Tyurin RMS(02) [mathematical]; Ritter mp/03; Konishi LNP(08)ht/07.
@ And sigma models: Witten PRD(79); Forgács et al PRL(80).
@ Quantization: Auzzi et al NPB(04)ht, Konishi proc(04)ht [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]; Bonati et al PRD(10)-a1009 [on the lattice].

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