YANG Yi-Song . ELECTRICALLY CHARGED SOLITONS IN GAUGE FIELD THEORY[J]. Acta mathematica scientia, Series B, 2010 , 30(6) : 1975 -2005 . DOI: 10.1016/S0252-9602(10)60186-5

[1]  Actor A.  Classical solutions of $SU(2)$ Yang--Mills theories. Rev Mod Phys, 1979, 51:  461--525

[2]  Adler S L. Monopoles and projective representations: two areas of influence of Yang-Mills theory on mathematics.
Preprint, arXiv:math-ph/0405049

[3]  Arafune J, Freund P G O, Goebel C J. Topology of Higgs fields. J Math Phys, 1975, 16:  433--437

[4]  Atiyah  M F, Ward R S. Instantons and algebraic geometry. Commun Math Phys, 1977,  55:  117--124

[5]  Bayen F, Flato M,  Fronsdal C, Lichnerowicz A, Sternheimer D. Deformation theory and quantization. I. Deformations of symplectic structures. Ann Phys, 1978, 111: 61--110

[6]  Bayen F, Flato M, Fronsdal C, Lichnerowicz A, Sternheimer D. Deformation theory and quantization. II. Physical applications. Ann Phys, 1978, 111: 111--151

[7]  Belavin A A, Polyakov A M, Schwartz A S, Tyupkin Yu S. Pseudoparticle solutions of the Yang-Mills equations. Phys Lett B, 1975, 59:   85--87

[8]  Bezryadina A, Eugenieva E, Chen Z. Self-trapping and flipping of double-charged vortices in optically induced photonic lattices. Optics Lett, 2006, 31:  2456--2458

[9]  Bogomol'nyi E B. The stability of classical solutions. Sov J Nucl Phys, 1976,  24: 449--454

[10]  Bramwell S T, Giblin S R, Calder S, Aldus R, Prabhakaran D, Fennell T. Measurement of the charge and current of magnetic monopoles in spin ice. Nature, 2009, 461: 956--959

[11]  Caffarelli L, Yang Y. Vortex condensation in the Chern--Simons Higgs model: an existence theorem. Commun Math Phys, 1995, 168:  321--336

[12]  Callias C. Axial anomalies and index theorems on open spaces. Commun Math Phys, 1978, 62:  213--234

[13]  Castelnovo C, Moessner R, Sondhi S L. Magnetic monopoles in spin ice. Nature, 2008, 451:  42--45

[14]  Chae D, Yu O. Imanuvilov, The existence of nontopological multivortex solutions in the relativistic self-dual Chern--Simons theory. Commun Math Phys, 2000, 215:  119--142

[15]  Chae D, Kim N. Topological multivortex solutions of the self-dual Maxwell--Chern--Simons--Higgs system. J Diff Eqs, 1997, 134: 154--182

[16]  Chan H, Fu C C, Lin  C S. Non-topological multivortex solutions to the self-dual Chern--Simons--Higgs equation. 
Commun Math Phys, 2002, 231: 189--221

[17]  Chen C C, Lin C S, Wang G. Concentration phenomena of two-vortex solutions in a Chern--Simons model. Ann Sc Norm Super Pisa Cl Sci, 2004, 3:  367--397

[18]  Chen R M, Guo Y, Spirn D, Yang Y. Electrically and magnetically charged vortices in the Chern--Simons--Higgs theory. Proc Roy Soc A, 2009, 465:  3489--3516

[19]  Chern J L, Chen  Z Y, Lin C S. Uniqueness of topological solutions and the structure of solutions for the Chern-Simons system with two Higgs particles. Commun Math Phys, 2010, 296: 323--351

[20]  Chern S S, Simons J. Some cohomology classes in principal fiber bundles and their application to Riemannian geometry. Proc Nat Acad Sci USA, 1971, 68: 791--794

[21]  Chern S S, Simons J. Characteristic forms and geometric invariants. Ann Math, 1974, 99: 48--69

[22]  Cho Y M, Kimm K. Electroweak monopoles. Preprint, arXiv:hep-th/9705213.

[23]  Cho Y M, Maison D. Monopole configuration in Weinberg--Salam model. Phys Lett B, 1997, 391:  360--365

[24]  Choe K. Uniqueness of the topological multivortex solution in the self-dual Chern-Simons theory. J Math Phys, 2005, 46:  012305

[25]  Choe K. Multiple existence results for the self-dual Chern-Simons-Higgs vortex equation. Comm Partial Diff Eqs, 2009, 34: 1465--1507

[26]  Choe K,  Kim N. Blow-up solutions of the self-dual Chern--Simons--Higgs vortex equation. Ann Inst H Poincarè--Anal Nonlinèaire, 2008, 25: 313--338

[27]  S. Coleman, Le monopôle magnètique cinquante ans aprè The magnetic monopole fifty years later]//Gauge Theories in High Energy Physics. Part I, II (Les Houches, 1981).  Amsterdam: North-Holland, 1983: 461--552

[28]  Curie P. On the possible existence of magnetic conductivity and free magnetism. Séances Soc Phys  (Paris), 1894:  76--77

[29]  Deser S, Jackiw R, Templeton S. Three-dimensional massive gauge theories. Phys Rev Lett, 1982, 48:  975--978

[30]  Deser S, Jackiw R, Templeton S. Topologically massive gauge theories. Ann Phys, 1982, 140:  372--411

[31]  Dirac P A M. Quantised Singularities in the electromagnetic field. Proc  Royal Soc A, 1931, 133:  60--72

[32]  Dunne G. Self-Dual Chern--Simons Theories. Lecture Notes in Physics, Vol  36. Berlin: Springer-Verlag, 1995

[33]  Dunne G. Mass degeneracies in self-dual models. Phys Lett B, 1995, 345: 452--457

[34]  Dunne G. Aspects of Chern-Simons theory. Preprint, arXiv: hep-th/9902115, Les Houches Lectures, 1998

[35]  Dziarmaga J. Low energy dynamics of [U(1)]^N Chern--Simons solitons. Phys Rev D, 1994, 49:  5469--5479

[36]  Dziarmaga J. Only hybrid anyons can exist in the broken symmetry phase of nonrelativistic [U(1)]² Chern--Simons theory. Phys Rev D, 1994, 50: R2376--R2380

[37]  Felsager B. Geometry, Particles, and Fields. Berlin, New York: Springer-Verlag, 1998

[38]  Forgacs P Horvath Z, Palla L. Exact multimonopole solutions in the Bogomolny-Prasad-Sommerfied limit. Phys Lett B, 1981, 99: 232--236

[39]  Fröhlich J, Marchetti P A. Quantum field theories of vortices and anyons. Comm Math Phys, 1989, 121: 177--223

[40]  Georgi H, Glashow S  L. Unified weak and electromagnetic interactions without neutral currents. Phys Rev Lett, 1972, 28: 1494--1497

[41]  Georgi H, Glashow S  L. Unity of all elementary-particle forces. Phys Rev Lett, 1974, 32:  438--441

[42]  Gingras M J P. Observing monopoles in a magnetic analog of ice. Science, 2009, 26: 375--376

[43]  Ginzburg  V L, Landau L D. On the theory of superconductivity//Collected Papers of L. D. Landau (edited by D. Ter Haar), New York: Pergamon, 1965: 546--568

[44]  Goddard P, Olive D I. Magnetic monopoles in gauge field theories. Rep Prog Phys, 1978, 41: 1357--1437

[45]  Greiner W, Müller B. Quantum Mechanics--Symmetries. 2nd ed. Berlin, New York: Springer-Verlag, 1994

[46]  Groenewold H J. On the principles of elementary quantum mechanics. Physica, 1946, 12:  405--460

[47]  Han J. Asymptotic limit for condensate solutions in the abelian Chern--Simons--Higgs model. Proc Amer Math Soc, 2003, 131:  1839--1845

[48]  Han J, Huh H. Self-dual vortices in a Maxwell-Chern-Simons model with non-minimal coupling. Lett Math Phys, 2007, 82: 9--24

[49]  Hirsch M. Differential Topology. New York, Heidelberg: Springer-Verlag,1976

[50]  Hong J, Kim Y, Pac  P Y. Multivortex solutions of the Abelian Chern--Simons--Higgs theory. Phys Rev Lett, 1990,  64: 2330--2333

[51]  Horvathy P A, Zhang P.  Vortices in (abelian) Chern-Simons gauge theory. Phys Rep, 2009, 481:  83--142

[52]  Huh H. Local and global solutions of the Chern-Simons-Higgs system. J Funct Anal, 2007, 242:  526--549

[53]  Humphreys J E. Introduction to Lie Algebras and Representation Theory. New York, Heidelberg:  Springer-Verlag,  1972

[54]  Inouye S, Gupta S, Rosenband T,  Chikkatur A P, Görlitz  A, Gustavson T L, Leanhardt A E, Pritchard D E, Ketterle W. Observation of vortex phase singularities in Bose-Einstein condensates. Phys Rev Lett, 2001, 87:  080402

[55]  Jackiw R. Quantum meaning of classical field theory. Rev Mod Phys, 1977, 49:  681--707

[56]  Jackiw R, Chern S S. Chern--Simons terms//Differential Geometry and Physics. Nankai Tracts Math 10.  Hackensack, NJ: World Sci Publ, 2006: 53--62

[57]  Jackiw R, Templeton S. How super-renormalizable interactions cure their infrared divergences. Phys Rev D,1981, 23: 2291--2304

[58]  Jackiw R,  Weinberg E J. Self-dual Chern--Simons vortices. Phys Rev Lett, 1990, 64: 2334--2337

[59]  Jacobs L,  Khare A, Kumar C N, Paul S K. The interaction of Chern--Simons vortices. Int J Mod Phys A, 1991, 6: 3441--3466

[60]  Jaffe A, Taubes C H.  Vortices and Monopoles. Boston: Birkhäuser, 1980

[61]  Jost  J, Wang G. Analytic aspects of the Toda system. I. A Moser-Trudinger inequality. Comm Pure Appl Math, 2001,  54: 1289--1319

[62]  Julia B, Zee A. Poles with both magnetic and electric charges in non-Abelian gauge theory. Phys Rev D, 1975, 11:  2227--2232

[63]  Kao H C, Lee K. Self-dual SU(3) Chern--Simons Higgs systems. Phys Rev D, 1994, f50: 6626--6632

[64]  Kawaguchi Y,  Ohmi T. Splitting instability of a multiply charged vortex in a Bose--Einstein condensate. Phys Rev A, 2004, 70:  043610

[65]  Khomskii D I, Freimuth A. Charged vortices in high temperature superconductors. Phys Rev Lett, 1995, 75: 1384--1386

[66]  Kim C, Lee C, Kao P, Lee B H, Min H.  Schrödinger fields on the plane with [U(1)]^N Chern--Simons interactions and generalized self-dual solitons. Phys Rev D, 1993, 48: 1821--1840

[67]  Kim  N. Existence of vortices in a self-dual gauged linear sigma model and its singular limit. Nonlinearity, 2006, 19:  721--739

[68]  Kontsevich M. Lecture Notes on Deformation Theory.  Berkeley, 1995

[69]  Kontsevich M. Formality conjecture//Gutt S, Rawnsley J, Sternheimer D, eds. Deformation Theory and Symplectic Geometry. Math Phys Stud 20. Dordrecht: Kluwer Acad Publ, 1997: 139--156

[70]  Kontsevich M. Deformation quantization of Poisson manifolds, I. Lett Math Phys, 2003, 66:  157--216

[71]  Kubo R. Wigner representation of quantum operators and its applications to electrons in a magnetic field. J Phys Soc Japan, 1964, 19:  2127--2139

[72]  Kumar C N,  Khare A. Charged vortex of finite energy in nonabelian gauge theories with Chern--Simons term. Phys Lett B, 1986, 178:  395--399

[73]  Lee K, Weinberg  E J. Nontopological magnetic monopoles and new magnetically charged black holes. Phys Rev Lett, 1994, 73: 1203--1206

[74]  Lai C H, ed.  Selected Papers on Gauge Theory of Weak and Electromagnetic Interactions. Singapore: World Scientific, 1981

[75]  Lin C S, Ponce A C, Yang Y. A system of elliptic equations arising in Chern--Simons field theory. J Funct Anal, 2007, 247: 289--350

[76]  Lin  C S, Prajapat J V.  Vortex condensates for relativistic abelian Chern-Simons model with two Higgs scalar fields and two gauge fields on a torus. Commun Math Phys, 2009, 288: 311--347

[77]  Lucia  M, Nolasco M. SU(3) Chern-Simons vortex theory and Toda systems. J Diff Eqs, 2002, 184: 443--474

[78]  Macri M, Nolasco M, Ricciardi T. Asymptotics for self-dual vortices on the torus and on the plane: a gluing technique. SIAM J Math Anal, 2005, 37:  1--16

[79]  Manton N. Complex structure of monopoles. Nucl Phys B, 1978, 135: 319--332

[80]  Manton N, Sutcliffe P. Topological Solitons. Cambridge Monographs on Mathematical Physics, Cambridge: Cambridge Univ Press, 2004

[81]  Matsuda Y, Nozakib K, Kumagaib K. Charged vortices in high temperature superconductors probed by nuclear magnetic resonance. J Phys Chem Solids, 2002, 63:  1061--1063

[82]  Mehra J, Rechenberg H. The Historical Development of Quantum Theory. Volume 6: The Completion of Quantum Mechanics 1926--1941. New York: Springer-Verlag, 2000

[83]  Milnor J W. Topology from the Differentiable Viewpoint. Charlottesville: University Press of Virginia, 1965

[84]  Milton K A. Theoretical and experimental status of magnetic monopoles. Rep Progress Phys, 2006, 69:  1637--1711

[85]  Morris DJ P, Tennant D A,  Grigera S A, Klemke B, Castelnovo C,  Moessner R, Czternasty C, Meissner M,  Rule K C,  Hoffmann J U, Kiefer K, Gerischer S, Slobinsky D, Perry R S. Dirac strings and magnetic monopoles in the spin ice Dy₂Ti₂O₇. Science, 2009, 326:  411--414

[86]  Moyal J E. Quantum mechanics as a statistical theory. Proc Cambridge Philosophical Soc, 1949, 45: 99--124

[87]  Nielsen H B, Olesen P.  Vortex-line models for dual strings. Nucl Phys B, 1973, 61: 45--61

[88]  Nolasco M. Nontopological N-vortex condensates for the self-dual Chern--Simons theory. Comm  Pure Appl Math,
2003, 56: 1752--1780

[89]  Nolasco M, Tarantello G. Double vortex condensates in the Chern--Simons--Higgs theory. Calc Var & PDE's, 1999, 9: 31--91

[90]  Nolasco M, Tarantello G. Vortex condensates for the SU(3) Chern--Simons theory. Commun Math Phys, 2000, 213: 599--639

[91]  Paul S,  Khare A. Charged vortices in an Abelian Higgs model with Chern--Simons term. Phys Lett B, 1986, 17: 420--422

[92]  Polyakov A M. Particle spectrum in quantum field theory. JETP Lett, 1974, 20:  194

[93]  Prasad M K, Sommerfield C M. Exact classical solutions for the 't Hooft monopole and the Julia--Zee dyon. Phys Rev Lett, 1975, 35:  760--762

[94]  Preskill J. Vortices and monopoles//Architecture of Fundamental Interactions at Short Distances. Les Houches, Session XLIV, 1985. Elsevier, 1987: 235--337

[95]  Ricciardi T, Tarantello G. Vortices in the Maxwell--Chern--Simons theory. Comm  Pure  Appl Math, 2000, 53:  811--851

[96]  Ryder L H. Quantum Field Theory. 2nd ed. Cambridge, U K: Cambridge Univ Press, 1996

[97]  Schechter M, Weder R. A theorem on the existence of dyon solutions. Ann Phys, 1981, 132: 293--327

[98]  Schonfeld J S. A massive term for three-dimensional gauge fields. Nucl Phys B, 1981, 185: 157--171

[99]  Schwinger J. Sources and magnetic charge. Phys Rev, 1968, 173:  1536--1544

[100]  Schwinger J. A magnetic model of matter. Science, 1969, 165: 757--761

[101]  Sokoloff J B. Charged vortex excitations in quantum Hall systems. Phys Rev B, 1985, 31:  1924--1928

[102]  Spruck J, Yang Y. Topological solutions in the self-dual Chern--Simons theory: existence and approximation. Ann Inst H Poincaré--Anal non linéaire, 1995, 12:  75--97

[103]  Spruck J, Yang Y. The existence of non-topological solitons in the self-dual Chern--Simons theory. Commun Math Phys, 1992, 149:  361--376

[104]  Spruck J, Yang Y.  Proof of the Julia--Zee theorem. Commun Math Phys, 2009, 291:  347--356

[105]  Sutcliffe P. BPS monopoles. Internat J Mod Phys A, 1997, 12:  4663--4706

[106]  Tarantello G. Multiple condensate solutions for the Chern--Simons--Higgs theory. J Math Phys, 1996, 37: 3769--3796

[107]  Tarantello G. Self-Dual Gauge Field Vortices.  Progress in Nonlinear Differential Equations and Their Applications 72. Boston: Birkhäuser, 2008

[108]  Taubes C H. The existence of multimonopole solutions to the nonabelian, Yang-Mills-Higgs equations for arbitrary simple gauge groups. Commun Math Phys, 1981, 80: 343--367

[109]  Taubes C H. The existence of a non-minimal solution to the SU(2) Yang--Mills--Higgs equations on R³, Part I.
Commun Math Phys, 1982, 86: 257--298

[110]  Taubes C H. Min-max theory for the Yang-Mills-Higgs equations. Commun Math Phys, 1985, 97:  473--540

[111]  Tchrakian D H. The 't Hooft electromagnetic tensor for Higgs fields of arbitrary isospin. Phys Lett B, 1980, 91:  415--416

[112]  t Hooft G.  Magnetic monopoles in unified gauge theories. Nucl Phys B, 1974, 79: 276--284

[113]  de Vega H J, Schaposnik F. Electrically charged vortices in non-Abelian gauge theories with Chern--Simons term. Phys Rev Lett, 1986, 56: 2564--2566

[114]  de Vega H J, Schaposnik F. Vortices and electrically charged vortices in non-Abelian gauge theories. Phys Rev D,  1986, 34: 3206--3213

[115]  Weinberg E J. Parameter counting for multimonopole solutions. Phys Rev D, 1979, 20:  936--944

[116]  Wells R O. Differential Analysis on Complex Manifolds. New York, Berlin: Springer-Verlag, 1980

[117]  Wilczek F. Quantum mechanics of fractional-spin particles. Phys Rev Lett, 1982, 49:  957--959

[118]  Wilczek F. Fractional Statistics and Anyon Superconductors. Singapore: World Scientific, 1990

[119]  Yang Y. The relativistic non-Abelian Chern--Simons equations. Commun Math Phys, 1997, 186:  199--218

[120]  Yang Y. Dually charged particle-like solutions in the Weinberg--Salam theory. Proc Roy Soc A, 1998, 454: 155--178

[121]  Yang Y. The Lee--Weinberg magnetic monopole of unit charge: existence and uniqueness. Physica D, 1998,  117:  215--240

[122]  ang Y. Coexistence of vortices and antivortices in an Abelian gauge theory. Phys Rev Lett, 1998, 80: 26--29

[123]  Yang Y. Strings of opposite magnetic charges in a gauge field theory. Proc Roy Soc A, 1999, 455: 601--629

[124]  Yang Y. Solitons in Field Theory and Nonlinear Analysis. Springer Monographs in Mathematics. New York: Springer-Verlag, 2001

[125]  Yang Y. On the deformation of some Lie algebras. Acta Math Sci, 1984, 4:  509--517

[126]  Zachos C, Fairlie  D, Curtright T. Quantum Mechanics in Phase Space. Singapore: World Scientific, 2005

[127]  Zwanziger D. Exactly soluble nonrelativistic model of particles with both electric and magnetic charges. Phys Rev, 1968, 176:  1480--1488

[128]  Zwanziger D. Quantum field theory of particles with both electric and magnetic charges. Phys Rev, 1968, 176: 1489--1495