Abstract
We describe the IOSp(D, 2∣2)-extension of the Poincaré group in the BRST- quantization of the (spinning) relativistic point particle. The Batalin-Fradkin- Vilkovisky method is used to construct the corresponding field theory, and its dimensional reduction by the Parisi-Sourlas mechanism is proven. We show that a certain element in the identity component of the SO(D, 2) subgroup of IOSp(D, 2∣2) induces the PCT-transformation in the physical subspace. We clarify the role of modular transformations (i.e., of world-line orientation-reversing diffeomorphisms) and argue that the PCT-transformation is the same as a modular transformation seen in an SO(D,2)-rotated frame.
In theories with chiral fermions, OSp(D, 2∣2) is typically broken down to O(D − 1, 1) ⊗ OSp(1, 1∣2), but modular invariance still seems to be at the heart of causality and PCT-invariance.
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References
C.A.P. Galvao, C. Teitelboim: J. Math. Phys. 21, 1863 (1980)
M. Henneaux, C. Teitelboim: Ann. Phys. 143, 127 (1982)
C. Teitelboim: Phys. Rev. D 25, 3159 (1982)
P.D. Mannheim: Phys. Lett. B 137, 385 (1984); B 166, 191 (1986)
S. Monaghan: Phys. Lett. B 178, 231 (1986); B 181, 101 (1986)
A. Neveu, P. West: Phys. Lett. B 182, 343 (1986)
A. Barducci, R. Casalbuoni, D. Dominici, R. Gatto: Phys. Lett. B 187, 135 (1987)
R. Casalbuoni: Talk given at the 12th Edicion De Los Encuentros relativistas (La Laguna, 1987)
T. Hori, C.B. Kim: Phys. Lett. B 207, 44 (1988)
A. Barducci, R. Casalbuoni, D. Dominici, R. Gatto: Phys. Lett. B 194, 257 (1987)
R. Casalbuoni, D. Dominici, R. Gatto, J. Gomis: Phys. Lett. B 198, 177 (1987); J. Gomis, J. Roca: Phys. Lett. B 207, 309 (1988)
A. Aratyn, R. Ingermanson, A.J. Niemi: Phys. Rev. Lett. 58, 965 (1987)
E.S. Egarian: Phys. Lett. B 202, 535 (1988); R.P. Manvelyan: Phys. Lett. B 205, 504 (1988)
T. Filk, H. Römer: Z. Phys. C 39, 203 (1988)
P. Thomi: J. Math. Phys. 30, 470 (1989)
A. Neveu, P. West: Nucl. Phys. B 293, 266 (1987)
W. Siegel, Introduction to String Field Theory (World Scientific, Singapore 1988) and references therein
E.S. Pradkin, G.A. Vilkovisky: Phys. Lett. B 55, 244 (1975); I. A. Batalin, G.A. Vilkovisky: Phys. Lett. B 69, 309 (1977); E. S. Fradkin, T.E. Pradkin: Phys. Lett. B 72, 343 (1978)
M. Henneaux: Phys. Rep. 126, 1 (1985)
E. Gozzi, M. Reuter: Nucl. Phys. B 320, 160 (1989)
E. Gozzi, M. Reuter: Nucl. Phys. B 325, 356 (1989)
J. Govaerts: preprints CERN-TH. 4950/88 and 5010/88
A.C. Hirshfeld: In The Fundamental Interaction - Geometrical Trends, Proceedings of the 1987 Bad Honnef meeting, ed. by J. Debrus and A.C. Hirshfeld ( Plenum Press, New York 1988 )
G. Parisi, N. Sourlas: Phys. Rev. Lett. 43, 744 (1979); Nucl. Phys. B 206, 321 (1982)
J.L. Cardy: Phys. Lett. B 125, 470 (1983)
B. Zumino (unpublished); G. Lüders: Ann. Phys. 2, 1 (1957); W. Pauli: in Niels Bohr and the Development of Physics, ed. by W. Pauli (McGraw-Hill, New York 1955); G. Lüders, B. Zumino: Phys. Rev. 106, 385 (1957); R. Jost: Helv. Phys. Acta 30, 409 (1957); R.F. Streater, A.S. Wightman: PCT, Spin and Statistics, and all that, ( Benjamin, New York, 1964 )
A. Barducci, R. Casalbuoni, L. Lusanna: Nuovo Cimento 35A, 377 (1976); F. A. Berezin, M.S. Marinov: Ann. Phys. 104, 336 (1977); L. Brink, S. Deser, B. Zumino, P. diVecchia, P. Howe: Phys. Lett. B 64, 435 (1976)
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© 1991 Springer-Verlag Berlin Heidelberg
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Reuter, M. (1991). Modular Invariance, Causality and the PCT-Theorem. In: Debrus, J., Hirshfeld, A.C. (eds) Geometry and Theoretical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76353-3_10
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DOI: https://doi.org/10.1007/978-3-642-76353-3_10
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