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Extensions of Gauge groups, related to quantum anomalies

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Abstract

An infinite-dimensional central extension of the group of currents is constructed, related to the anomaly in the Gauss law, discovered by L. D. Faddeev.

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Literature cited

  1. 1.

    L. D. Faddeev, “Operator anomaly for Gauss' law,” Phys. Lett.,145B, No. 1–2, 81–84 (1984).

  2. 2.

    A. G. Reiman, M. A. Semenov-Tyan-Shanskii, and L. D. Faddeev, “Quantum anomalies and cocycles on gauge groups,” Funkts. Anal. Prilozhen.,18, No. 4, 64–72 (1984).

  3. 3.

    R. Stora, “Algebraic structure and topological origin of anomalies,” in: Progress in Gauge Field Theory (Cargese, 1983), Plenum, New York (1984), pp. 543–562.

  4. 4.

    L. D. Faddeev and S. L. Shatashvili, “Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies,” Teor. Mat. Fiz.,60, No. 2, 206–217 (1984).

  5. 5.

    G. Segal, “Faddeev's anomaly in Gauss's law,” Preprint, Oxford (1985).

  6. 6.

    D. B. Fuks, The Cohomology of Infinite-Dimensional Lie Algebras [in Russian], Nauka, Moscow (1984).

  7. 7.

    A. Guichardet, Cohomologie des Groupes Topologigues et des Algebres de Lie, CEDIC, Paris (1980).

  8. 8.

    G. B. Segal, “A classifying space of a topological group in the Gel'fand-Fuks sense,” Funkts. Anal. Prilozhen.,9, No. 2, 48–50 (1975).

  9. 9.

    C. C. Moore, “Group extensions and cohomology for locally compact groups. III,” Trans. Am. Mat. Soc.,221, No. 1, 1–33 (1976).

  10. 10.

    S. P. Novikov, “The Hamiltonian formalism and a multivalued analogue of Morse theory,” Usp. Mat. Nauk,37, No. 5, (227) 3–49 (1982).

  11. 11.

    R. Bott, “Lectures on characteristic classes and foliations,” Lect. Notes Math., No. 279, 1–94 (1972).

  12. 12.

    S. Smale, “On the structure of manifolds,” Am. J. Math.,84, 387–399 (1962).

  13. 13.

    J. L. Dupont, Curvature and Characteristic Classes, Lect. Notes Math., No. 640, Springer, Berlin (1978).

  14. 14.

    T. R. Ramadas, “The Wess-Zumino term and Fermionic solitons,” Commun. Math. Phys.,93, 355–365 (1984).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 146, pp. 102–118, 1985.

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Reiman, A.G. Extensions of Gauge groups, related to quantum anomalies. J Math Sci 40, 80–93 (1988). https://doi.org/10.1007/BF01084940

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Keywords

  • Gauge Group
  • Central Extension
  • Quantum Anomaly