Abstract
We present an exact solution of the anomalous chiral Schwinger model using Fermionic variables. We implement infrared regularization by considering the model on a spatial circleS 1. Quantum effects modify the gauge constraints through the appearance of Schwinger terms in the gauge algebra. We perform a careful analysis of the resulting second class gauge constraints by implementing Dirac's method at the quantum level and obtain the spectrum of the theory. We get a consistent unitary Lorentz invariant theory for particular values of the counterterms. We find that when we regulate the fermionic sector of the model without reference to the gauge fields Lorentz invariance requires that we add both Lorentz variant and gauge variant counterterms.
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C. Bouchiat, J. Iliopoulos, Ph. Meyer: Phys. Lett. 38B (1972) 519; H. Georgi, S. Glashow: Phys. Rev. D6 (1972) 429; D. Gross, R. Jackiw: Phys. Rev. D6 (1972) 477
M. Green, J. Schwarz: Phys. Lett. 149B, 117
W.A. Bardeen, A.R. White (eds.): Symposium on Anomalies, Geometry, Topology 1985 Symposium on Topological Methods in Field Theory, Helsinki, Finland (to be published)
J. Schwinger: Phys. Rev. 128 (1962) 2425
C. Hagen: Ann. Phys. 81 (1973) 67
R. Jackiw, R. Rajaraman: Phys. Rev. Lett. 54 (1985) 1219
L. Fadeev, V. Popov: Phys. Lett. 25B (1967) 29
O. Babelon, F. Shaposnik, C. Viallet: Phys. Lett. B 177 (1986) 385
R. Rajaraman: Phys. Lett. 154B (1985) 305, H. O. Girotti, H.J. Rothe, K.D. Rothe; Phys. Rev. D33 (1986) 514, D34 (1986) 592
J.G. Halliday, E. Rabinovici, A. Schwimmer, M. Chanowitz: Nucl. Phys. B268 (1986) 413
D. Boyanovsky: Nucl. Phys. B294 (1987) 223
A. Niemi, G. Semenoff: Phys. Lett. B 175 (1986) 439
M. Paranjape: Universite de Montreal Preprint
P. Dirac: Can. J. Math. 2 (1950) 129; A. Hanson, T. Regge, C. Teitelboim: Acad. Naz. Lincei (Rome) (1976)
N. Manton: Ann. Phys. 159 (1985) 220
Fradkin, Vilkoviski: CERN report, 1979 unpublished
K. Fujikawa: Phys. Rev. Lett. 42 (1979) 1195
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Supported in part by the Natural Sciences and Engineering Research Council of Canada
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Link, R., Roberge, A. & Semenoff, G.W. Lorentz invariant exact solution of the anomalous chiral Schwinger model. Z. Phys. C - Particles and Fields 39, 269–273 (1988). https://doi.org/10.1007/BF01551003
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DOI: https://doi.org/10.1007/BF01551003