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Particle picture in external fields, quantum holonomy, and gauge anomaly

Abstract

We formulate a path integral of chiral gauge theories by means of the canonical quantization of fermions in time-dependent background gauge fields. The expression of the path integral is composed of two parts. One is due to the nontrivial holonomy of the fermionic Fock vacua and the other is the conventional form which is used in the perturbation theory. The nontrivial holonomy part is expected to be a nonlocal counter term. We show a possibility of the perturbative calculation

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References

  1. 1.

    See the articles in Current Algebra and Chiral Anomaly, R. Jackiw, R. Treiman, and E. Witten (eds.), World Scientific, Singapore, 1985.

  2. 2.

    See the articles in Invariant Wave Equations, G. Velo and A. S. Wightman (eds.), Lectures Notes in Physics 73, Springer-Verlag, Berlin, 1978, and references cited therein.

  3. 3.

    Ohnuki, Y. and Kashiwa, T., Prog. Theor. Phys. 60, 548 (1978).

  4. 4.

    Faddeev, L. D. and Shatashvili, S. L., Theor. Math. Phys. 60, 770 (1984); Faddeev, L. D., Phys. Lett. 145B, 81 (1984); Nelson, P. and Alvarez-Gaume L., Commun. Math. Phys. 99, 103 (1985); Niemi, A. J. and Semenoff, G. W., Phys. Rev. Lett. 55, 926 (1985); Sonoda, H., Phys. Lett. 156B, 220 (1985); Nucl. Phys. 266, 410 (1986); Hosono, S., DPNU-86-44 (1986).

  5. 5.

    Labonté, G., Commun. Math. Phys. 36, 59 (1974).

  6. 6.

    Dirac, P. A. M., The Principles of Quantum Mechanics, Oxford University Press, Oxford, 1958.

  7. 7.

    Stone, M., Phys. Rev. D33 1191 (1986).

  8. 8.

    Chang, L. N. and Liang, Y., Commun. Math. Phys. 108, 139 (1987).

  9. 9.

    Wess, J. and Zumino, B., Phys. Lett. 37B, 95 (1971). Witten, E., Nucl. Phys. B223, 422 (1983).

  10. 10.

    Faddeev, L. D., Theor. Math. Phys. 1, 3 (1967).

  11. 11.

    Faddeev, L. D. and Shatashvili, S. L., Phys. Lett. 167B, 225 (1986); Niemi, A. J. and Semenoff, G. W., Phys. Rev. Lett. 56, 1019 (1986); Babelon, O., Schaposnik, F. A., and Viallet, C. M., Phys. Lett. 177B, 385 (1986); Harada, K. and Tsutsui, I., Phys. Lett. 183B, 311 (1987).

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Odaka, K., Itoh, T. Particle picture in external fields, quantum holonomy, and gauge anomaly. Lett Math Phys 15, 297–303 (1988). https://doi.org/10.1007/BF00419587

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Keywords

  • Statistical Physic
  • Gauge Theory
  • Perturbation Theory
  • Group Theory
  • External Field