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

  • Gauge Theories I
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Gauge Theory and Gravitation

Part of the book series: Lecture Notes in Physics ((LNP,volume 176))

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References

  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 (NY) 140, 372 (1982); H. Nielsen and H. Woo (unpublished).

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  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.

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  3. R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976); R. Jackiw, Rev. Mod. Phys. 52, 661 (1980).

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  4. S. Chern, “Complex Manifolds without Potential Theory”, 2 ed. Springer Verlag, Berlin, 1979.

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  5. See Deser, Jackiw and Templeton, Ref. 1; Deser, Ref. 2.

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  6. The canonical description is due to J. Goldstone and E. Witten unpublished; for details see Jackiw, Ref. 2(second cited work).

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  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condition has been obtained by E. Witten in a 4-dimensional SU(2) gauge theory, Princeton University preprint (unpublished).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.

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Authors and Affiliations

  1. Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

    R. Jackiw

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  1. R. Jackiw
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Keiji Kikkawa Noboru Nakanishi Hidekazu Nariai

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© 1983 Springer-Verlag

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Jackiw, R. (1983). Massive gauge theories in three dimensions (= at high temperature). In: Kikkawa, K., Nakanishi, N., Nariai, H. (eds) Gauge Theory and Gravitation. Lecture Notes in Physics, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11994-9_7

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  • DOI: https://doi.org/10.1007/3-540-11994-9_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11994-4

  • Online ISBN: 978-3-540-39470-9

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