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Gauge Theory

  • Chapter
Principal Bundles

Part of the book series: Universitext ((UTX))

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Abstract

If this were a novel, then this chapter would be the climax of the story, because here we present the now-legendary result identifying the gauge fields of physics theory with the principal bundles that have a connection of mathematical theory. But in science the story continues and continues. And to this day we do not know how it will end.

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Bibliography

  1. W. Drechsler and M.E. Mayer, Fiber Bundle Techniques in Gauge Theory, Lecture Notes in Physics, Vol. 67, Springer, 1977.

    Google Scholar 

  2. C. Ehresmann, Les connexiones infinitésimales dans un espace fibré différentiable, in: Colloque de topologie, Bruxelles (1950), pp. 29–55, Masson, Paris, 1951.

    Google Scholar 

  3. B.C. Hall, Lie Groups, Lie Algebras, and Representations, Springer, 2003.

    Google Scholar 

  4. G. ’t Hooft, Gauge theories of the forces between elementary particles, Sci. Am. 243 (1980) 104–138.

    Google Scholar 

  5. G. ’t Hooft editor, 50 Years of Yang–Mills Theory, World Scientific, 2005.

    Google Scholar 

  6. E. Lubkin, Ann. Phys. (N.Y.) 23 (1963) 233.

    Google Scholar 

  7. L. O’Raifeartaigh, The Dawning of Gauge Theory, Princeton University Press, 1997.

    Google Scholar 

  8. R. Penrose, The Road to Reality, Knopf, 2005.

    Google Scholar 

  9. R. Utiyama, Invariant theoretical interpretation of interaction, Phys. Rev. 101 (1956) 1597–1607.

    Article  MathSciNet  Google Scholar 

  10. S. Weinberg, The Quantum Theory of Fields, Vol. II, Modern Applications, Cambridge University Press, 1996.

    Book  Google Scholar 

  11. H. Weyl, Gravitation und Elektrizität, Sitz. König. Preuss. Akad. Wiss. 26 (1918) 465–480.

    MATH  Google Scholar 

  12. T.T. Wu and C.N. Yang, Dirac monopole without strings: monopole harmonics, Nucl. Phys. B 107 (1976) 365–380.

    Article  MathSciNet  Google Scholar 

  13. C.N. Yang and R.L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954) 191–195.

    Article  MathSciNet  Google Scholar 

  14. D.Z. Zhang, C.N. Yang and contemporary mathematics, Math. Intelligencer 15, no. 4, (1993) 13–21.

    Google Scholar 

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico

    Stephen Bruce Sontz

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  1. Stephen Bruce Sontz
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© 2015 Springer International Publishing Switzerland

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Sontz, S.B. (2015). Gauge Theory. In: Principal Bundles. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-14765-9_14

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