From superconductors and four-manifolds to weak interactions

Witten, Edward

doi:10.1090/S0273-0979-07-01167-6

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From superconductors and four-manifolds to weak interactions

Author: Edward Witten
Journal: Bull. Amer. Math. Soc. 44 (2007), 361-391
MSC (2000): Primary 81Q99, 53D45
Posted: April 23, 2007
MathSciNet review: 2318156
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Abstract: The goal of this article is to describe the concept of ``gauge symmetry breaking'' and its applications to superconductors, four-manifold theory, and particle physics.

1. P. W. Anderson, Plasmons, gauge invariance, and mass, Phys. Rev. (2) 130 (1963), 439–442. MR 0153388 (27 #3355)
2. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. (2) 108 (1957), 1175–1204. MR 0095694 (20 #2196)
3. E. B. Bogomol′nyĭ, The stability of classical solutions, Jadernaja Fiz. 24 (1976), no. 4, 861–870 (Russian); English transl., Soviet J. Nuclear Phys. 24 (1976), no. 4, 449–454. MR 0443719 (56 #2082)
4. P. A. M. Dirac, ``The Quantum Theory of the Electron,'' Proc. Roy. Soc. (London) A117 (1928) 610.
5. S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), no. 3, 257–315. MR 1066174 (92a:57035), http://dx.doi.org/10.1016/0040-9383(90)90001-Z
6. F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons, Phys. Rev. Lett. 13 (1964), 321–323. MR 0174314 (30 #4520)
7. V. Ginzburg and L. Landau, ``On the Theory of Superconductivity,'' JETP 20 (1950) 1064-1082.
8. H. Georgi and S. L. Glashow, ``Unity of All Elementary Particle Forces,'' Phys. Rev. Lett. 32 (1974) 438-441.
9. S. L. Glashow, ``Partial Symmetries of Weak Interactions,'' Nucl. Phys. 22 (1961) 579-588.
10. M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718 (87j:53053), http://dx.doi.org/10.1007/BF01388806
11. LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/.
12. Peter W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett. 13 (1964), 508–509. MR 0175554 (30 #5738)
13. Gregory Moore and Edward Witten, Integration over the 𝑢-plane in Donaldson theory, Adv. Theor. Math. Phys. 1 (1997), no. 2, 298–387. MR 1605636 (99k:57070)
14. A. Salam and J. C. Ward, Electromagnetic and weak interactions, Phys. Lett. 13 (1964), 168–171. MR 0192825 (33 #1050)
15. A. Salam, ``Weak and Electromagnetic Interactions,'' in N. Svartholm, ed., Elementary Particle Physics (Almqvist and Wiksells, Stockholm, 1968), 367-377.
16. Julian Schwinger, Gauge invariance and mass, Phys. Rev. (2) 125 (1962), 397–398. MR 0154597 (27 #4543)
17. Alexandru Scorpan, The wild world of 4-manifolds, American Mathematical Society, Providence, RI, 2005. MR 2136212 (2006h:57018)
18. N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in 𝑁=2 supersymmetric Yang-Mills theory, Nuclear Phys. B 426 (1994), no. 1, 19–52. MR 1293681 (95m:81202a), http://dx.doi.org/10.1016/0550-3213(94)90124-4
19. Clifford Henry Taubes, Arbitrary 𝑁-vortex solutions to the first order Ginzburg-Landau equations, Comm. Math. Phys. 72 (1980), no. 3, 277–292. MR 573986 (83c:81124)
20. Clifford Henry Taubes, The Seiberg-Witten and Gromov invariants, Math. Res. Lett. 2 (1995), no. 2, 221–238. MR 1324704 (96a:57076)
21. Clifford Henry Taubes, Seiberg Witten and Gromov invariants for symplectic 4-manifolds, First International Press Lecture Series, vol. 2, International Press, Somerville, MA, 2000. Edited by Richard Wentworth. MR 1798809 (2002j:53115)
22. S. Weinberg, ``A Model of Leptons,'' Phys. Rev. Lett. 19 (1967) 1264.
23. S. Weinberg, The Quantum Theory of Fields, volumes 1 and 2 (Cambridge University Press, 1996).

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