Massive gauge theories in three dimensions (= at high temperature)

  • R. Jackiw
Gauge Theories I
Part of the Lecture Notes in Physics book series (LNP, volume 176)


Gauge Theory Gauge Transformation Mass Term Gauge Field Lagrange Density 
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  1. 1.
    W. Siegel, Nucl. Phys. B156, 135 (1979); R. Jackiw and S. Templeton, Phys. Rev. D23, 2291 (1981); J. Schonfeld, Nucl. Phys. B185, 157 (1981); S. Deser, R. Jackiw and S. Templeton, Phys. Rev. Lett. 48, 975 (1982) and Ann. Phys. (NY) 140, 372 (1982); H. Nielsen and H. Woo (unpublished).CrossRefGoogle Scholar
  2. 2.
    Other reviews are R. Jackiw in “Asymptotic Realms of Physics” (A. Guth, K. Huang, and R. Jaffe, editors), MIT Press, Cambridge, MA, 1983 and Arctic Summer School Proceedings (1982); S. Deser, DeWitt Festschrift, to appear.Google Scholar
  3. 3.
    R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976); R. Jackiw, Rev. Mod. Phys. 52, 661 (1980).Google Scholar
  4. 4.
    S. Chern, “Complex Manifolds without Potential Theory”, 2 ed. Springer Verlag, Berlin, 1979.Google Scholar
  5. 5.
    See Deser, Jackiw and Templeton, Ref. 1; Deser, Ref. 2.Google Scholar
  6. 6.
    The canonical description is due to J. Goldstone and E. Witten unpublished; for details see Jackiw, Ref. 2(second cited work).Google Scholar
  7. 7.
    An analogous quantization condition has been obtained by E. Witten in a 4-dimensional SU(2) gauge theory, Princeton University preprint (unpublished). One begins with the observation that Π4(SU(2)) = Π4(S3) = cyclic group of two integers, to conclude that the 4-dimensional gauge functions U(t,\(\vec x\)) fall into two homotopically distinct classes. Next one finds that when N species of left-handed Weyl fermions in the fundamental [doublet] representation are coupled to the SU(2) gauge field, their functional [fermionic] determinant is not invariant against homotopically non-trivial gauge transformations. Rather it changes by the factor (−1)N; hence N must be even.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • R. Jackiw
    • 1
  1. 1.Center for Theoretical Physics Laboratory for Nuclear Science and Department of PhysicsMassachusetts Institute of TechnologyCambridge

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