BRST quantization of topological field theory

Wei Chen

doi:10.1103/PhysRevD.41.1172

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BRST quantization of topological field theory

Wei Chen^*

Department of Physics, University of Utah, Salt Lake City, Utah 84112

^*On leave of absence from the Institute of High-Energy Physics, Academia Sinica, Beijing, People's Republic of China.

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Phys. Rev. D 41, 1172 – Published 15 February, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.1172

Abstract

The canonical quantization of the topological field-theory model $\int M F \land B$ , proposed by Horowitz, is examined through the Becchi-Rouet-Stora-Tyutin approach. With this approach we have a manifestly covariant description of a certain class of topological quantum field theories. However, if $M$ in the present model is any orientable four-dimensional manifold, one would end up with different theories when different polarizations are chosen. Therefore a restriction $M = R^{1} \times Σ$ , as pointed out by Horowitz, is required for consistency.

References (14)

E. Witten, Commun. Math. Phys. 117, 353 (1988)
E. Witten, Commun. Math. Phys. 121, 351 (1989)
A. Belavin, A. M. Polyakov, and A. Zamolodchikov, Nucl. Phys. B241, 333 (1984)
G. Horowitz, NSF Report No. ITP-88-178 (unpublished) G. Horowitz and M. Srednicki, UCSB Report No. TH-89-14 (unpublished)
W. Chen, G. Semenoff, and Y-S. Wu, University of Utah report, 1989 (unpublished)
C. Becchi, A. Rouet, and R. Stora, Ann. Phys. (N.Y.) 98, 287 (1976) I. V. Tyutin, Lebedev Report No. FIAN No. 39, 1975 (unpublished)
E. S. Fradkin and G. A. Vilkovisky, Phys. Lett. 55B, 224 (1975) I. A. Batalian and G. A. Vilkovisky, ibid. 69B, 309 (1977) E. S. Fradkin and T. E. Fradkina, ibid. 72B, 343 (1978) I. A. Batalin and E. S. Fradkin, ibid. 122B, 157 (1983) M. Henneaux, Phys. Rep. 126, 1 (1985)
T. Kugo and I. Ojima, Prog. Theor. Phys. Suppl. 66, 1 (1979) T. Kugo and S. Uehara, Nucl. Phys. B197, 378 (1982) L. Baulieu, Phys. Rep. 129, 1 (1985) I. A. Batalin and G. A. Vilkovisky, Phys. Lett. 102B, 27 (1981) I. A. Batalin and E. S. Fradkin, Phys. Rev. D 28, 2567 (1983) J. Math. Phys. 25, 2426 (1984) J. M. L. Fisch and M. Henneaux, Brussels report, 1988 (unpublished)
C. Crnkovic and E. Witten, Princeton report, 1986 (unpublished) C. Zuckerman, in Mathematical Aspects of String Theory, proceedings of the Conference, San Diego, California, 1986, edited by S.-T. Yau (Advanced Series in Mathematical Physics, Vol. 1) (World Scientific, Singapore, 1987)
W. Chen, W. L. Shen, and Y. Yu, Phys. Rev. D 39, 1210 (1989)
P. K. Townsend, Phys. Lett. 88B, 97 (1979) T. Kimura, Prog. Theor. Phys. 64, 357 (1980) ibid.65, 338 (1981)
W. Chen and Y. Yu, Phys. Rev. D 35, 3915 (1987)
P. A. M. Dirac, Lecture on Quantum Mechanics (Yeshiva University) (Academic, New York, 1967)
E. Guadagnini, M. Martellini, and M. Mintchev, Phys. Lett. B 227, 111 (1989) Report No. IFUP-TH6/89 (unpublished)

[c1] E. Witten, Commun. Math. Phys. 117, 353 (1988)

[c2] E. Witten, Commun. Math. Phys. 121, 351 (1989)

[c3] A. Belavin, A. M. Polyakov, and A. Zamolodchikov, Nucl. Phys. B241, 333 (1984)

[c4] G. Horowitz, NSF Report No. ITP-88-178 (unpublished) G. Horowitz and M. Srednicki, UCSB Report No. TH-89-14 (unpublished)

[c5] W. Chen, G. Semenoff, and Y-S. Wu, University of Utah report, 1989 (unpublished)

[c6] C. Becchi, A. Rouet, and R. Stora, Ann. Phys. (N.Y.) 98, 287 (1976) I. V. Tyutin, Lebedev Report No. FIAN No. 39, 1975 (unpublished)

[c7] E. S. Fradkin and G. A. Vilkovisky, Phys. Lett. 55B, 224 (1975) I. A. Batalian and G. A. Vilkovisky, ibid. 69B, 309 (1977) E. S. Fradkin and T. E. Fradkina, ibid. 72B, 343 (1978) I. A. Batalin and E. S. Fradkin, ibid. 122B, 157 (1983) M. Henneaux, Phys. Rep. 126, 1 (1985)

[c8] T. Kugo and I. Ojima, Prog. Theor. Phys. Suppl. 66, 1 (1979) T. Kugo and S. Uehara, Nucl. Phys. B197, 378 (1982) L. Baulieu, Phys. Rep. 129, 1 (1985) I. A. Batalin and G. A. Vilkovisky, Phys. Lett. 102B, 27 (1981) I. A. Batalin and E. S. Fradkin, Phys. Rev. D 28, 2567 (1983) J. Math. Phys. 25, 2426 (1984) J. M. L. Fisch and M. Henneaux, Brussels report, 1988 (unpublished)

[c9] C. Crnkovic and E. Witten, Princeton report, 1986 (unpublished) C. Zuckerman, in Mathematical Aspects of String Theory, proceedings of the Conference, San Diego, California, 1986, edited by S.-T. Yau (Advanced Series in Mathematical Physics, Vol. 1) (World Scientific, Singapore, 1987)

[c10] W. Chen, W. L. Shen, and Y. Yu, Phys. Rev. D 39, 1210 (1989)

[c11] P. K. Townsend, Phys. Lett. 88B, 97 (1979) T. Kimura, Prog. Theor. Phys. 64, 357 (1980) ibid.65, 338 (1981)

[c12] W. Chen and Y. Yu, Phys. Rev. D 35, 3915 (1987)

[c13] P. A. M. Dirac, Lecture on Quantum Mechanics (Yeshiva University) (Academic, New York, 1967)

[c14] E. Guadagnini, M. Martellini, and M. Mintchev, Phys. Lett. B 227, 111 (1989) Report No. IFUP-TH6/89 (unpublished)

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