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Introduction to the fiber-bundle approach to gauge theories

Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 67)

Keywords

Gauge Theory Gauge Group Vector Bundle Gauge Field Chern Class 
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Bibliography

  1. Arnol'd, V. I.: Matematicheskie metody klassicheskoi mekhaniki (Mathematical methods of classical mechanics), Nauka, Moscow, 1974.Google Scholar
  2. Bourbaki, N: Variétés différentielles et analytiques, Hermann, Paris, §§ 1–7, 1967, §§ 8–15, 1971.Google Scholar
  3. Chern, S-S.: The Geometry of Characteristic Classes, in Proc. of the 13-th Biennial Seminar, Canadian Math. Congress, Montreal, pp. 1–40.Google Scholar
  4. Chevalley, C.: Theory of Lie Groups, vol. I, Princeton U. Press, Princeton, 1946.Google Scholar
  5. De Rham, G.: Variétés différentiables, Hermann, Paris, 1955.Google Scholar
  6. Dieudonné, J.: Treatise on Analysis, Academic Press, N. Y., vol III, 1972, vol. IV, 1974 (vols. V, VI in French).Google Scholar
  7. Greub, W., S. Halperin, and R. Vanstone: Connections, Curvature, and Cohomology, Academic Press, N. Y., Vol. I., 1972, Vol. II, 1973, Vol. 111, 1974.Google Scholar
  8. Hawking, S. W., and G. F. R. Ellis: The Large-Scale Structure of the Universe, Cambridge University Press, 1973.Google Scholar
  9. Hermann, R.: Vector Bundles in Mathematical Physics, Benjamin, N.Y. and a large number of other books by the same author.Google Scholar
  10. Hirsch, M.: Differential Topology, Springer Verlag, N. Y., 1976.Google Scholar
  11. Hirzebruch, F.: Topological Methods in Algebraic Geometry, 3-rd ed. Springer Verlag, Berlin, 1966.Google Scholar
  12. Husemoller, D.: Fibre Bundles, 2-nd ed., Springer Verlag, N. Y. 1975.Google Scholar
  13. Kobayasi, S., and K. Nomizu, Foundations of Differential Geometry, Wiley, N. Y., Vol. I, 1963, Vol, 11,1969.Google Scholar
  14. Landau, L. D., and E. M. Lifshitz: Teoriya polya (Classical Field Theory) 6-th ed., Nauka, Moscow, 1973; Engl. Transl, Pergamon Press.Google Scholar
  15. Lichnerowicz, A.: Theorie globale des connexions et des groupes d'holonomie, Ed. Cremonese, Roma, 1955.Google Scholar
  16. Lightman, A. P., W. H. Press, R. H. Price, and S. A. Teukolsky:Problem Book in Relativity and Gravitation, Princeton U. P.,1975.Google Scholar
  17. Mayer, M. E.: Cîmpuri cuantice si particlee elementare (Quantized fields and elementary particles), Ed. Tehnica, Bucharest, 1969.Google Scholar
  18. Misner, C. W., R. S. Thorne, and J. A. Wheeler, Gravitation, Freeman, San Francisco, 1973.Google Scholar
  19. Pauli, W.: Die allgemeinen Prinzipien der Quantenmechanik, Handb. d. Physik, 2-nd ed., Bd. V, T. 1, Springer Verlag, Berlin, 1958.Google Scholar
  20. Spivak, M.:A Comprehensive Introduction to Differential Geometry, 3 vols., Publish or Perish, Waltham, 1971. Also: Calculus on Manifolds, Benjamin, 1969.Google Scholar
  21. Steenrod, N.; The Topology of Fibre Bundles, Princeton Univ. Press, 1951.Google Scholar
  22. Sternberg, S: Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, 1963.Google Scholar
  23. Sulanke, R., and P. Wintgen, Differentialgeometrie und Faserbündel, Birkhäuser Verlag, Basel 1972.Google Scholar
  24. Vranceanu, G.: Lecons de geometrie differentielle, 3 vols. Ed. de l'Academie de la R. P. Roumaine, Bucharest/Gauthier-Villars, Paris, 1964 (also available in German and the Romanian original).Google Scholar
  25. Yang, C. N.: Lecture notes on gauge theories and fiber bundles (approximate title), University of Hawaii, 1975.Google Scholar
  26. Milnor, J. W., and J. D. Stasheff: Characteristic Classes, Princeton Univ. Press, 1974.Google Scholar
  27. E. Abers and B. W. Lee, Gauge Theories, Phys. Reports, 9, No l, 1–141 (1973).Google Scholar
  28. W. Ambrose and I. M. Singer, A Theorem on Holonomy, Trans. Amer. Math. Soc. 75, 428–443 (1953).Google Scholar
  29. R. L. Arnowitt and S. I. Fickler, Phys. Rev. 127, 1821 (1962).Google Scholar
  30. A. A. Belavin, A. M. Polyakov, A. S. Schwartz and S. Tyupkin, Pseudoparticle Solutions of the Yang-Mills Equations, Phys. Lett. 59B, 85 (1976).Google Scholar
  31. J. Bernstein, Spontaneous Symmetry Breaking, Gauge Theories, Higgs Mechanism and All That, Rev. Mod. Phys. 46, 1 (1974).Google Scholar
  32. K. Bleuler, Helv. Phys. Acta 23, 567 (1950).Google Scholar
  33. R. Balian, J. Drouffe and C. Itzykson, Gauge Fields on a Lattice, Phys. Rev. D10, 3376 (1974); D11, 2098 (1975).Google Scholar
  34. R. Bott and S. S. Chern, Hermitian Vector Bundles and the Equidistribution of Zeroes of their Holomorphic Sections, Acta Mathem. 114, 71–112 (1965).Google Scholar
  35. R. Brout and F. Englert, Phys. Rev. Lett. 13, 321 (1964).Google Scholar
  36. C. Callan, R. F. Dashen and D. J. Gross, The Structure of the Gauge Theory Vacuum, Phys. Lett. 63B, 334 (1976); A Mechanism for Quark Confinement, Princeton Preprint COO-2220-94, 1977.Google Scholar
  37. S. Coleman, Classical Lumps and their Quantum Descendants, Erice Lecture Notes, 1975.Google Scholar
  38. B. S. De Witt. Phys. Rev. 162, 1195, 1239 (1967).Google Scholar
  39. S. Doplicher, R. Haag and J. E. Roberts, Fields, Observables, and Gauge Transformations, I, II, Commun. Math. Phys. 13, 1–23 (1969); 15, 173–200 (1971). Local Observables and Particle Statistics, I, Ibid. 23, 199–230 (1971); S. Doplicher and J. E. Roberts, Fields, Statistics and Nonabelian Gauge Groups, Ibid. 28, 331–348 (1972). Lectures by S. Doplicher at various conferences.Google Scholar
  40. L. D. Faddeev, Lecture at the Mathematical Physics Conference, Moscow, 1972; published in the Trudy Matem. Inst. im. Steklova (in Russian) 1975.Google Scholar
  41. L. D. Faddeev and V. S. Popov, Feynman Diagrams for the Yang-Mills Field, Phys. Lett. 25B, 29 (1967); Kiev Preprint, 1967; L. D. Faddeev, Teor. Matem. Fiz, l, 3 (1969) [Theor. Math. Phys. 1, 1 (1969)].Google Scholar
  42. E. Fermi, Rev. Mod. Phys. 4, 87 (1932).Google Scholar
  43. R. P. Feynman, Acta Physica Polonica 26, 697 (1963).Google Scholar
  44. P. L. Garcia, Gauge Algebras, Curvature and Symplectic Structure to appear in J, Differ. Geom.; Reducibility of the Symplectic Structure of Classical Fields, Proc. of the Symposium on Differential-Geometrical Methods in Physics, Bonn, 1975, K. Bleuler and A. Reetz, eds., Springer Lecture Notes in Math., 1977.Google Scholar
  45. L. Gårding and A. S. Wightman, Fields as operator-Valued Distributions in Relativistic Quantum Field Theory, Arkiv för Fysik 28, 129–184 (1964).Google Scholar
  46. M. Gell-Mann and S. L. Glashow, Ann. Phys. (N. Y.) 15, 437 (1961).Google Scholar
  47. J. Glimm and A. Jaffe, Quark Trapping for Lattice U(1) Gauge Fields, Harvard Preprint, 1977. Functional Integral Methods in Quantum Field Theory, Cargese 1976 Lectures, to be published.Google Scholar
  48. S. N. Gupta, Proc. Phys. Soc. (Lond.) 61A, 68 (1950).Google Scholar
  49. G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964).Google Scholar
  50. S. W. Hawking, Gravitational Instantons, Phys. Lett. 60A, 81 (1977).Google Scholar
  51. P. W. Higgs, Phys. Rev. Lett. 12, 132 (1964); Phys. Rev. 145, 1156 (1966)Google Scholar
  52. R. Jackiw and C. Rebbi, Vacuum Periodicity in a Yang-Mills Theory, Phys. Rev. Lett. 37, 172 (1976). conformal Properties of a Yang-Mills Pseudoparticle, Phys. Rev. D 14, 517 (1976).Google Scholar
  53. H. Kerbrat-Lunc, Ann. Inst. H. Poincaré 13A, 295 (1970).Google Scholar
  54. R. Kerner, Ann. Inst. H. Poincaré 9A, 143 (1968).Google Scholar
  55. T. W. B. Kibble, J. Math. Phys. 2, 212 (1961).Google Scholar
  56. T. W. B. Kibble, Phys. Rev. 155, 1554 (1967).Google Scholar
  57. H. G. Loos, Internal Holonomy Groups of Yang-Mills Fields, J. Math. Phys. 8, 2114–2124 (1967); Phys. Rev. 188, 2342 (1969).Google Scholar
  58. Lu Qi-keng, Gauge Fields and Connections in Principal Bundles, Chin. J. Phys. 23, 153–161 (1975) [Wuli Xuebao 23, 249–263 (1974)]Google Scholar
  59. E. Lubkin, Ann. Phys. (N. Y.) 23, 233 (1963).Google Scholar
  60. V. Lugo, Holes and Integrality of the Curvature, UCLA Preprint, TEP/8, May 1976.Google Scholar
  61. W. Marciano and H. Pagels, Chiral Charge Conservation and Gauge Fields, Phys. Rev. (1976), idem and Z. Parsa, Multiply Charged Magnetic Monopoles, SU (3) Pseudoparticles and Gravitational Pseudoparticles, Rockefeller Preprint C00-2232B-108, 1976.Google Scholar
  62. M. E. Mayer, Thesis, Unpublished, Univ. of Bucharest, 1956; Extended Invariance Properties of Quantized Fields, I, Preprint JINR, Dubna 1958 and Nuovo Cimento 11, 760–770 (1959).Google Scholar
  63. M. E. Mayer, C*-Bundles and Symmetries in Algebraic Quantum Field Theories, Proc. of Conf. on Noncompact Groups in Physics, Y. Chow, ed., Milwaukee, 1965; W. A. Benjamin, N. Y. 1966. Fibrations, Connections and Gauge Theories (An Afterthought to the Talk by A. Trautman, Proc. of the International Symposium on New Mathematical Methods in Physics, Bonn 1973, K. Bleuler and A. Reetz, eds. Talk at the Intern. Congr. of Mathematicians (Abstract N4), Vancouver, B. C., 1974. Gauge Fields as Quantized Connection Forms, Proc. of the Symposium on Differential-Geometrical Methods in Physics, Bonn, 1975, K. Bleuler and A. Reetz, eds., Lecture Notes in Mathematics, Springer Verlag, Berlin, 1977.Google Scholar
  64. M. E. Mayer, Gauge Fields and Characteristic Classes, to be published.Google Scholar
  65. A. A. Migdal, Rekursionnye uravneniya v kalibrovochnykh teoriyakhpolya (Recursion Ecuations in Gauge Field Theories), Zh. Eksp. Teor. Fiz. 69, 810–822 (1975) [Sov. Phys. JETP 42, 413–418 (1976)].Google Scholar
  66. E. Noether, Invariante Variationsprobleme, Nachr. Ges. Göttingen (math.-phys. Klasse) 1918, 235–257.Google Scholar
  67. V. I. Ogievetskii and I. V. Polubarinov, Zh. Eksp. Teor. Fiz. 41, 247 (1961) [Sov. Phys. JETP 14, 179 (1962)].Google Scholar
  68. K. Osterwalder, Gauge Theories on the Lattice, Cargese Lectures, 1976, to be published.Google Scholar
  69. A. M. Polyakov, JETP Lett. 20, 194 (1974); Sov. Phys. JETP 41, 988 (1975); Phys. Lett. 59B, 80, 82 (1975). Nordita Preprint,1976.Google Scholar
  70. M. Prasad and C. Sommerfield, Phys. Rev. Lett. 35, 760 (1975).Google Scholar
  71. J. E. Roberts, Local Cohomology and Superselection, Preprint,1976.Google Scholar
  72. A. Salam and J. C. Ward, Nuovo Cimento 11, 568 (1959).Google Scholar
  73. A. Salam, Nobel Symposium, 1968, Almquist & Wiksell, Stockholm.Google Scholar
  74. J. Schwinger, Phys. Rev. 82, 914 (1951); 125, 1043; 127, 324 (1962); 91, 714 (1953).Google Scholar
  75. I. E. Segal, Proc. Nat. Acad. Sci. USA 41, 1103 (1955); 42, 670 (1956). Quantization of Nonlinear Systems, J. Math. Phys. 1, 468–488 (1960); Quantized Differential Forms, Topology 7, 147–171 (1968).Google Scholar
  76. F. Strocchi, The Existence of Local Solutions to the Equations ∂μFμν = jν and□φ = j in QFT, Princeton Seminar Notes 1971-72.Google Scholar
  77. F. Strocchi and A. S. Wightman, Proof of the Charge Superselection Rule in Local Relativistic Quantum Field Theory, J. Math. Phys. 15, 2198–2224 (1974).Google Scholar
  78. W. E. Thirring, Ann. Phys. (N. Y.) 16, 96 (1961).Google Scholar
  79. G. 't Hooft, Nucl. Phys. B33, 173; B35, 167 (1971).Google Scholar
  80. G. 't Hooft, Symmetry Breaking through Bell-Jackiw Anomalies, Phys. Rev. Lett. 37, 8 (1976). Computation of Quantum Effects due to a Four-Dimensional Pseudoparticle, Harvard Preprint, 1976. Cal-Tech Seminar, 1976.Google Scholar
  81. G.'t Hooft and M. Veltman, Nucl. Phys. B44, 189 (1973).Google Scholar
  82. A. Trautman, Infinitesimal Connections in Physics, Proc. Internat. Symposium on New Mathem. Methods in Physics, Bonn 1973, K. Bleuler and A. Reetz, eds., Bonn., 1973, and earlier work quoted there.Google Scholar
  83. R. Utiyama, Invariant Theoretical Interpretation of Interaction, Phys. Rev. 101, 1597 (1956).Google Scholar
  84. M. Veltman, Nucl. Phys. B21, 288 (1971).Google Scholar
  85. S. Weinberg, A Theory of Leptons, Phys. Rev. Lett. 19, 1264 (1967).Google Scholar
  86. S. Weinberg, Rev. Mod. Phys. 46, 255 (1974).Google Scholar
  87. H. Weyl, Gravitation and Elektrizität, Sber. Preuss. Akad. Wiss. 1918, 465–480; Z. Physik 56, 330 (1929).Google Scholar
  88. T. T. Wu and C. N. Yang, Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields Phys. Rev. 12D, 3845 (1975).Google Scholar
  89. C. N. Yang and R. L. Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Phys. Rev. 96, 191 (1954).Google Scholar
  90. C. N. Yang, Integral Formalism for Gauge Fields, Phys. Rev. Lett. 33, 445–447 (1974).Google Scholar
  91. Albeverio, S. A., and Høegh-Krohn, R. J.: Mathematical Theory of Feynman Path Integrals, LNM 523, Springer Verl., 1976.Google Scholar
  92. Feynman, R. P., and Hibbs, A. R.: Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965Google Scholar
  93. Palais, R. S.: Seminar on the Atiyah-Singer Index Theorem, Princeton Univ. Press, 1965.Google Scholar
  94. M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Deformations of Instantons (Oxford-Berkeley-MIT Preprint, recd. May 1977).Google Scholar
  95. L. S. Brown, R. D. Carlitz, and C. Lee, Massless Excitations in Instanton Fields (U. of Washington Preprint, recd. May 1977).Google Scholar
  96. C. G. Callan,Jr., R. Dashen, and D. J. Gross, A Mechanism for Quark Confinement (IAS Preprint,C00-2220-94, 1977).Google Scholar
  97. V. De Alfaro, S. Fubini, and G. Furlan, A New Classical Solution for The Yang-Mills Equation, Phys. Lett. 65B, 163 (1976).Google Scholar
  98. S. Fubini, A New Approach to Conformal Invariant Field Theories, Nuovo Cimento 34A, 521 (1976). V. De Alfaro, S. Fubini,and G. Furlan, Conformal Invariance in Quantum Mechanics, Nuovo Cimento 34A, 569 (1976).Google Scholar
  99. R. Jackiw, C. Nohl, and C. Rebbi, Phys. Rev D (to appear), and R. Jackiw and C. Rebbi, Phys. Lett. B (to appear), both quoted in [65].Google Scholar

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