Abstract
It has been recognized for some time now that the BRST method provides one of the most powerful tools for quantizing theories endowed with a local gauge freedom. This method is extremely useful not only in the path-integral approach, but also in the operator formalism.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. S. Fradkin and M. A. Vasiliev, Phys. Lett. 72B, 70 (1977); G. Sterman, P. K. Townsend, and P. van Nieuwenhuizen, Phys. Rev. D17, 1501 (1978); R. E. Kallosh, Nucl. Phys. B141, 141 (1978).
M. B. Green and J. H. Schwarz, Phys. Lett. 136B, 367 (1984).
L. Brink and J. H. Schwarz, Phys. Lett. 100B, 310 (1981); W. Siegel, Phys. Lett. 128B, 397 (1983). For more information on the off-shell closure of the gauge algebra of the superpar-ticle, see L. Brink and M. Henneaux, Principles of String Theory, Plenum Press, New York (1988); U. Lindström, M. Roček, W. Siegel, P. van Nieuwenhuizen, and A. E. van de Ven, Phys. Lett. 224B, 285 (1989).
R. P. Feynman, Acta Phys. Polon. 24, 697 (1963); L. D. Faddeev and V. N. Popov, Phys. Lett. 25B, 30 (1967); B. S. De Witt, Phys. Rev. 162, 1195 (1967); 1239.
E. S. Fradkin and G. A. Vilkovisky, Phys. Lett. 55B, 224 (1975); I. A. Batalin and G. A. Vilkovisky, Phys. Lett. 69B, 309 (1977); E. S. Fradkin and T. E. Fradkina, Phys. Lett. 72B, 343 (1978); I. A. Batalin and E. S. Fradkin, Phys. Lett. 122B, 157 (1983).
I. A. Batalin and G. A. Vilkovisky, Phys. Lett. 102B, 27 (1981); 120B, 166 (1983); Phys. Rev. D28, 2567 (1983); J. Math. Phys. 26, 172 (1985).
R. E. Kallosh, Nucl. Phys. B141, 141 (1978).
B. de Wit and J. W. van Holten, Phys. Lett. 79B, 389 (1979); J. W. van Holten, “On the construction of supergravity theories,” Chapter V, Ph.D. Thesis (Leiden, 1980).
M. Henneaux, Phys. Rep. 126, 1 (1985); I. A. Batalin and E. S. Fradkin, Rev. Nuovo Cimento 9, 1 (1986); M. Henneaux, Classical Foundations of BRST Symmetry, Bibliopolis, Naples (1988).
B. S. De Witt, in Dynamical Theory of Groups and Fields (B. S. De Witt and C. M. De Witt eds.), Gordon and Breach, New York (1965); Phys. Rev. 162 1195 (1967)
A. S. Schwarz, Lett. Math. Phys. 2, 247 (1978); J. Schonfeld, Nucl. Phys. B185, 157 (1981); S. Deser, R. Jackiw, and S. Templeton, Phys. Rev. Lett. 48, 372 (1984); Ann. Phys. (NY) 140, 372 (1984); E. Witten, Commun. Math. Phys. 121, 351 (1989).
B. L. Voronov and I. V. Tyutin, Theoret and Math. Phys. 50, 218 (1982).
I. A. Batalin and G. A. Vilkovisky, Nucl. Phys. B234, 106 (1984).
M. Henneaux, C. Teitelboim, and J. Zanelli, Nucl. Phys. B332, 169 (1990). Related works include J. L. Anderson and P. G. Bergmann, Phys. Rev. 83, 1018 (1951); N. Mukunda, Phys. Scr. 21, 783 (1980); L. Castellani, Ann. Phys. (NY) 143, 357 (1982); C. Batlle, J. Gomis, X. Gracia, and J. M. Pons, J. Math. Phys. 30, 1345 (1989); and references therein.
P. A. M. Dirac, Canad. J. Math. 2, 129 (1950); “Lectures on Quantum Mechanics,” Yeshiva University (1964).
R. E. Peierls, Proc. R. Soc. London A214, 143 (1952).
Č. Crnković and E. Witten, in Newton’s Tercentenary Volume (S. Hawking and W. Israel, eds.), Cambridge University Press, Cambridge (1988).
G. J. Zuckerman, “Action Principles and Global Geometry,” Proc. Conf. Math. Aspects of String Theory, San Diego, 1986 (S. T. Yau, ed.), World Scientific, Singapore (1987).
A. Ashtekar, L. Bombelli, and R. Kour, in “Physics of Space,” Proc. of Maryland Meeting 1986 (Kim and Zachary, eds.), Springer Verlag, Berlin (1988).
M. Henneaux, Commun. Math. Phys. 140, 1 (1991).
W. Siegel, Nucl. Phys. B238, 307 (1984).
J. Fisch and M. Henneaux, Commun. Math. Phys. 128, 627 (1990).
M. Henneaux and C. Teitelboim, in Quantum Mechanics of Fundamental Systems (C. Teitelboim and J. Zanelli, eds.), Plenum Press, New York (1989).
J. L. Koszul, Bull Soc. Math. France 78, 5 (1950).
A. Borel, Ann. Math. 57, 115 (1953).
J. Tate, Illinois J. Math. 1, 14 (1957).
J. Fisch, M. Henneaux, J. Stasheff, and C. Teitelboim, Commun. Math. Phys. 120, 379 (1989).
J. D. Stasheff, Trans. Amer. Math. Soc. 18, 215, 293 (1963); V. K. A. M. Gugenheim and J. P. May, Mem. Amer. Math. Soc. 142, 1 (1974); V. K. A. M. Gugenheim and J. D. Stasheff, Bull. Soc. Math. Belg. Sér A 38, 237 (1986).
M. Henneaux and C. Teitelboim, Commun. Math. Phys. 115, 213 (1988).
J. Stasheff, Bull. Amer. Math. Soc. 19, 287 (1988).
T. Kugo and S. Uehara, Nucl. Phys. B197, 378 (1982); F. R. Ore and P. van Nieuwenhuizen, Nucl. Phys. B204, 317 (1982); L. Alvarez-Gaumé and L. Baulieu, Nucl. Phys. B212, 255 (1983).
W. Siegel, Stony Brook preprint ITP-SB-89-14 (1989).
C. Batlle, J. Gomis, J. París, and J. Roca, Barcelona preprint UB-ECM-PF 2/89 (1989).
J. Fisch and M. Henneaux, Phys. Lett. 226B, 80 (1989).
G.’ t Hooft, in Recent Developments in Gravitation (M. Lévy and S. Deser, eds.), Plenum Press, New York (1979).
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965).
J. Alfaro and P. H. Damgaard, Phys. Lett. 222B, 425 (1989); J. Alfaro, private communication (1989).
J. Zinn-Justin, in Trends in elementary particle theory, Lecture Notes in Physics vol. 37 (H. Rollnik and K. Dietz, eds.), Springer, Berlin (1975).
J. A. Dixon, Nucl. Phys. B99, 420 (1975).
W. Siegel, Phys. Lett. 93B, 275 (1980); J. Thierry-Mieg and L. Baulieu, Nucl. Phys. B228, 259 (1985); L. Baulieu and J. Thierry-Mieg, Phys. Lett. 144B, 221 (1983).
M. Asorey and F. Falceto, Global Aspects of Covariant Quantization of Gauge Theories, Harvard preprint HUPT 88/A039.
P. Hirschfeld, Nucl. Phys. B157, 37 (1979); K. Fujikawa, Prog. Theor. Phys. 61, 627 (1979).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Henneaux, M. (1992). The Antifield-BRST Formalism for Gauge Theories. In: Teitelboim, C., Zanelli, J. (eds) Quantum Mechanics of Fundamental Systems 3. Series of the Centro de Estudios Científicos de Santiago. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3374-0_6
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3374-0_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6489-4
Online ISBN: 978-1-4615-3374-0
eBook Packages: Springer Book Archive