Massive gauge theories in three dimensions (= at high temperature)
Part of the Lecture Notes in Physics book series (LNP, volume 176)
Gauge Theories I
KeywordsGauge Theory Gauge Transformation Mass Term Gauge Field Lagrange Density
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- 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 (NY) 140, 372 (1982); H. Nielsen and H. Woo (unpublished).CrossRefGoogle Scholar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.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.R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976); R. Jackiw, Rev. Mod. Phys. 52, 661 (1980).Google Scholar
- 4.S. Chern, “Complex Manifolds without Potential Theory”, 2 ed. Springer Verlag, Berlin, 1979.Google Scholar
- 5.See Deser, Jackiw and Templeton, Ref. 1; Deser, Ref. 2.Google Scholar
- 6.The canonical description is due to J. Goldstone and E. Witten unpublished; for details see Jackiw, Ref. 2(second cited work).Google Scholar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.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condition has been obtained by E. Witten in a 4-dimensional SU(2) gauge theory, Princeton University preprint (unpublished).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
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