Literature Cited
J. M. Souriau, Structure des Systems Dynamiques, Dunod, Paris (1970).
B. Kostant, Lect. Notes Math.,170, 87 (1970).
A. A. Kirillov, Usp. Mat. Nauk,17, 57 (1962).
A. A. Kirillov, Elements of Representation Theory [in Russian], Nauka, Moscow (1978); Modern Problems of Mathematics. Fundamental Directions, Vol. 22 [in Russian], VINITI, Moscow (1987), pp. 5–162.
A. A. Kirillov, Modern Problems of Mathematics. Fundamental Directions, Vol. 4 [in Russian], VINITI, Moscow (1985), pp. 141–178.
N. M. J. Woodhouse, Geometric Quantization, Clarendon, Oxford (1980); J. Sniatycki, Geometric Quantization and Quantum Mechanics, Springer, Berlin (1980); N. Hart, Geometric Quantization in Action [Russian translation], Mir, Moscow (1985).
L. Baulieu, Phys. Rep.,129, 1 (1985).
M. Henneaux, Phys. Rep.,126, 1 (1985).
V. I. Arnol'd and A. B. Givental', in: Modern Problems of Mathematics. Fundamental Directions, Vol. 4 [in Russian], VINITI, Moscow (1985), pp. 7–139.
M. J. Bowick and S. G. Rajeev, Nucl. Phys. B,296, 1007 (1988).
A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1988). (Translation of earlier edition: Gauge Fields, Introduction to Quantum Theory (Frontiers in Physics, Vol. 50), Reading, Mass. (1980).)
A. D. Popov, Teor. Mat. Fiz.,83, 384 (1990).
A. D. Popov, Yad. Fiz.,52, 907 (1990).
A. D. Popov, Mod. Phys. Lett. A,5, 2057 (1990).
R. S. Ward, Phys. Lett. A,81, 81 (1977); Complex Manifold Techniques in Theoretical Physics, Pitman, San Francisco (1979), pp. 12–34.
M. F. Atiyah, N. J. Hitchin, and J. Singer, Proc. R. Soc. London, Ser. A,362, 425 (1978).
Yu. I. Manin, Gauge Fields and Complex Geometry [in Russian], Nauka, Moscow (1984).
R. Penrose and W. Rindler, Spinors and Space-Time, Vol. 2, C. U. P., Cambridge (1986).
Twistors and Gauge Fields [collection of Russian translations], Mir, Moscow (1983).
R. Penrose, Gen. Relat. Grav.,7, 31 (1976).
M. F. Atiyah, V. G. Drinfeld, N. J. Hitchin, and Yu. I. Manin, Phys. Lett. A,65, 185 (1978).
A. G. Sergeev, in: Monopoles: Topological and Variational Methods [Russian translation], Mir, Moscow (1989), pp. 492–555.
L. P. Hughston, in: Complex Manifold Techniques in Theoretical Physics, Pitman, San Francisco (1979), pp. 115–125; Lect. Notes Phys.,97, 1 (1979).
S. Salamon, Invent. Math.,67, 143 (1982).
L. B. Berard and T. Ochiai, in: Glob. Riem. Geom. Symp., New York (1984), pp. 52–59.
N. R. O'Brien and J. H. Rawnsley, in: Ann. Global Anal. Geom.,3, 29 (1985); J. Rawnsley, Lect. Notes Math.,1263, 97 (1987).
S. A. Merkulov, Yad. Fiz.,51, 1445 (1990).
R. S. Ward, Nucl. Phys. B,236, 381 (1984).
S. Salamon, in: Glob. Riem. Geom. Symp., New York (1984), pp. 65–74, Ann. Sci. Ec. Norm. Sup.,19, 31 (1986); S. G. Gindikin, Funktsional. Analiz i Ego Prilozhen.,20, 82, (1986); B. Chow and D. Yang, J. Diff. Geom.,29, 361 (1989); S. A. Merkulov, Funktsional. Analiz i Ego Prilozhen.,24, 84 (1990).
C. Okonek and H. Spindler, J. für die Reine und Angew. Math.,364, 35 (1986); I. Nitta, Proc. Jpn. Acad. A,63, 23, 327 (1987); Tôhoku Math. J.,40, 425 (1988); M. M. Carpia and S. M. Salamon, Nonlinearity,1, 517 (1988); J. F. Glazenbrook, Rep. Math. Phys.,25, 141 (1988).
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vols. 1 and 2, Interscience, New York (1963).
S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs (1964).
N. Bourbaki, Éléments de Mathématiques. Variétés Différentielles et Analytiques. Fasc. de Résultats, Paris (1967).
A. Pressley and G. Segal, Loop Groups, O.U.P. 91986).
R. J. Blattner, Lect. Notes Math.,570, 11 (1977).
T. Maebashi, Math. J. Okayama Univ.,12, 91 (1966); H. Rossi, Trans. Am. Math. Soc.,263, 207 (1981).
R. J. Blattner and J. H. Rawnsley, J. Funct. Anal.,50, 188 (1983); Bull. Soc. Math. Belg. B,38, 109 (1986).
P. Topilawa, Invent. Math.,89, 425 449 (1987).
N. J. Hitchin, contemp. Math.,58, 157 (1986); N. J. Hitchin, A. Karlhede, U. Lindström, and M. Roček, Commun. Math. Phys.,108, 535 (1987).
R. Wells, Differential Calculus on Complex Manifolds [Russian translation], Mir, Moscow (1976).
K. Kodaira and D. C. Spencer, Ann. Math.,67, 328, 403 (1958);71, 43 (1960); K. Kodaira, Am. J. Math.,85, 79 (1963).
C. P. Boyer, Lect. Notes Phys.,189, 25 (1983).
B. Kostant and S. Sternberg, Ann. Phys.,176, 49 (1987); R. Loll, Commun. Math. Phys.,119, 509 (1988).
V. G. Kac and D. H. Peterson, Proc. Nat. Acad. Sci. USA,78, 3308 (1981).
I. A. Batalin and G. A. Vilkovisky, Phys. Lett. B,102, 27 (1981); Phys. Rev. D,28, 2567 (1983); Nucl. Phys. B,234, 106 (1984); J. Math. Phys.,26, 172 (1985).
Additional information
Vladimir Polytechnic Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 87, No. 1, pp. 3–21, April, 1991.
Rights and permissions
About this article
Cite this article
Popov, A.D. Generalized twistors and geometric quantization. Theor Math Phys 87, 331–344 (1991). https://doi.org/10.1007/BF01016571
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01016571