- Access by Xinjiang University
Constrained partition functions and the antisymmetric tensor field
Phys. Rev. D 42, 2040 – Published 15 September, 1990
DOI: https://doi.org/10.1103/PhysRevD.42.2040
Abstract
We consider the case when the spatial topology of the Universe is that of a torus with metric . We form an expression for the density of states under the constraint that the total momentum and winding number are zero. To accomplish this we introduce nonzero values of , , and in the imaginary-time formalism and integrate over all such values.
References (33)
- K. Kikkawa and M. Yamasaki, Phys. Lett. 149B, 357 (1984) N. Sakai and I. Senda, Prog. Theor. Phys. 75, 692 (1986) V. P. Nair, A. Shapere, A. Strominger, and F. Wilczek, Nucl. Phys. B287, 414 (1987) B. Sathiapalan, Phys. Rev. Lett. 58, 1597 (1987)
- R. Brandenberger and C. Vafa, Nucl. Phys. B316, 391 (1989)
- M. Dine, P. Huet, and N. Seilberg, Nucl. Phys. B322, 301 (1989)
- R. Dijkgraaf, E. Verlinde, and H. Verlinde, Commun. Math. Phys. 115, 649 (1988)
- A. Giveon, E. Rabinovici, and G. Veneziano, Nucl. Phys. B322, 167 (1989) A. Shapere and F. Wilczek, ibid. B320, 669 (1989)
- J. Molera and B. Ovrut, Phys. Rev. D 40, 1146 (1989)
- J. Dai, R. Leigh, and J. Polchinski, Mod. Phys. Lett. A 4, 2073 (1989)
- R. Hagedorn, Nuovo Cimento A 64, 1640 (1969)
- K. Huang and S. Weinberg, Phys. Rev. Lett. 25, 895 (1970)
- S. Frautschi, Phys. Rev. D 3, 2821 (1971)
- S. Carlitz, Phys. Rev. D 5, 3231 (1972)
- E. Alverez, Phys. Rev. D 31, 418 (1985)
- B. Sundborg, Nucl. Phys. B254, 583 (1985)
- M. Bowick and L. Wijewardhana, Phys. Rev. Lett. 54, 2485 (1985)
- S. Tye, Phys. Lett. 158B, 388 (1985)
- J. Polchinski, Commun. Math. Phys. 104, 37 (1986)
- P. Salomonson and B. Skagerstam, Nucl. Phys. B268, 349 (1986)
- B. McClain and B. Roth, Commun. Math. Phys. 111, 539 (1987)
- B. Sathiapalan, Phys. Rev. D 35, 3277 (1987)
- K. O'Brien and C. Tan, Phys. Rev. D 36, 1184 (1987)
- D. Mitchell and N. Turok, Phys. Rev. Lett. 58, 1577 (1987) Nucl. Phys. B294, 1139 (1987)
- J. Atick and E. Witten, Nucl. Phys. B310, 291 (1988)
- M. McGuigan, Phys. Rev. D 38, 552 (1988)
- N. Deo, S. Jain, and C. I. Tan, Phys. Lett. B 220, 125 (1989)
- C. I. Tan, in Particles, Strings and Supernovae, proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Providence, Rhode Island, 1988, edited by A. Jevicki and C-I. Tan (World Scientific, Singapore, 1989)
- N. Turok, in Proceedings of the Workshop on Thermal Fields, Cleveland, Ohio [Physica A 158, 516 (1989)]
- M. Bowick and S. Giddings, Nucl. Phys. B325, 631 (1989) S. Giddings, Phys. Lett. B 226, 55 (1989) N. Deo, S. Jain, and C. Tan, Phys. Rev. D 40, 2626 (1989)
- K. Narain, M. Simaldi, and E. Witten, Nucl. Phys. B279, 369 (1987)
- H. Elze, W. Greiner, and J. Rafelski, Phys. Lett. 124B, 515 (1983) Z. Phys. C 24, 361 (1984)
- K. Shiraishi, Il Nuovo Cimento A 100, 683 (1988)
- L. Brink and H. B. Nielsen, Phys. Lett. 43B, 419 (1973) F. Dyson, in Symmetries in Particle Physics, edited by I. Bars, A. Chodos, and C. Tze (Plenum, New York, 1984), p. 275 D. Cepner and E. Witten, Nucl. Phys. B278, 493 (1986)
- C. P. Burgess, N. Hambli, and A. Kshirsager, McGill University Report No. 88-0807, 1988 (unpublished) Class. Quantum Grav. 6, 1473 (1989)
- P. Gribosky, J. Donoghue, and B. Holstein, Ann. Phys. (N.Y.) 190, 149 (1989)