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BRST cohomology and Hilbert spaces of non-abelian models in the decoupled path integral formulation. (English) Zbl 0924.58008

Summary: The existence of several nilpotent Noether charges in the decoupled formulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate this matter in the context of simple quantum mechanical and field theoretical models, where the structure of the Hilbert space is known. We provide a systematic procedure for deciding which of the BRST conditions is to be imposed on the physical states in order to ensure the equivalence of the decoupled formulation to the original, coupled one. \(\copyright\) Academic Press.

MSC:

58D30 Applications of manifolds of mappings to the sciences
81T70 Quantization in field theory; cohomological methods
81V05 Strong interaction, including quantum chromodynamics
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References:

[2] Belvedere, L. V.; Rothe, K. D.; Swieca, J. A.; Schroer, B., Nucl. Phys. B, 153, 112 (1979)
[3] Roskies, R.; Schaposnik, F. A., Phys. Rev. D, 23, 558 (1981)
[4] Abdalla, E.; Rothe, K. D., Phys. Lett. B, 363, 85 (1995)
[5] Lowenstein, J. H.; Swieca, J. A., Ann. Phys. (N.Y.), 68, 172 (1971)
[6] Abdalla, E.; Abdalla, M. C.B., Phys. Rep., 265, 254 (1996)
[7] Abdalla, E.; Abdalla, M. C.B., Phys. Lett. B, 337, 347 (1994)
[8] Int. J. Mod. Phys. A, 10, 1611 (1995)
[9] Gawedski, K.; Kupianen, A., Nucl. Phys. B, 320, 625 (1989)
[10] Phys. Lett. B, 215, 119 (1988)
[11] Karibali, D.; Park, Q.; Schnitzer, H. J.; Yang, Z., Phys. Lett. B, 216, 307 (1989)
[12] Aharony, O.; Ganor, O.; Sonnenschein, J.; Yankielowicz, S., Nucl. Phys. B, 399, 527 (1993)
[13] Karibali, D.; Schnitzer, H. J., Nucl. Phys. B, 329, 649 (1990)
[14] Cabra, D. C.; Rothe, K. D.; Schaposnik, F. A., Int. J. Mod. Phys. A, 11, 3379 (1996) · Zbl 1044.81744
[15] Damgaard, P. H.; Nielsen, H. B.; Sollacher, R., Nucl. Phys. B, 385, 227 (1992)
[16] Theron, A. N.; Schaposnik, F. A.; Scholtz, F. G.; Geyer, H. B., Nucl. Phys. B, 437, 187 (1995)
[17] Damgaard, P. H.; Sollacher, R., Nucl. Phys. B, 433, 671 (1995)
[18] Alfaro, J.; Damgaard, P. H., Ann. Phys. (N.Y.), 202, 398 (1990)
[19] Scholtz, F. G.; Theron, A. N.; Geyer, H. B., Phys. Lett. B, 345, 242 (1995)
[20] Ring, P.; Schuck, P., The Nuclear Many-Body Problem (1980), Springer-Verlag: Springer-Verlag Heidelberg
[21] Klauder, J. R.; Skagerstam, B. S., Coherent States (1985), World Scientific: World Scientific Singapore
[22] Feynman, R. P.; Hibbs, A. R., Quantum Mechanics and Path Integrals (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0176.54902
[23] Balachandran, A. P.; Marmo, G.; Skagerstam, B. S.; Stern, A., Classical Topology and Quantum States (1991), World Scientific: World Scientific Singapore · Zbl 0754.53058
[24] Henneaux, M.; Teitelboim, C., Quantization of Gauge Systems (1992), Princeton University Press: Princeton University Press Cambridge · Zbl 0838.53053
[25] Witten, E., Comm. Math. Phys., 92, 455 (1984)
[26] Wess, J.; Zumino, B., Phys. Lett. B, 37, 95 (1971)
[27] Abdalla, E.; Rothe, K. D., Phys. Rev. D, 36, 3190 (1987)
[29] Bastianelli, F., Nucl. Phys. B, 361, 555 (1991)
[30] Tanii, Y., Mod. Phys. Lett. A, 5, 927 (1990)
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