메뉴 건너뛰기




Volumn 326, Issue 1-3, 2000, Pages 1-163

Geometry of the physical phase space in quantum gauge systems

Author keywords

Constrained systems; Dirac quantization; Gauge theories; Gribov problem; Orbit space; Path integral

Indexed keywords


EID: 0034147118     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(99)00085-X     Document Type: Review
Times cited : (35)

References (249)
  • 2
    • 34547361024 scopus 로고
    • R.P. Feynman, Rev. Mod. Phys. 20 (1948) 367. R.P. Feynman, Phys. Rev. 84 (1951) 108. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965. The idea of using the classical action in quantum mechanics was first proposed by Dirac in P.A.M. Dirac, Phys. Z. Sowietunion 3 (1933) 64 (reprinted in: J. Schwinger, Quantum Electrodynamics, Dover, New York, 1958).
    • (1948) Rev. Mod. Phys. , vol.20 , pp. 367
    • Feynman, R.P.1
  • 3
    • 36149017199 scopus 로고
    • R.P. Feynman, Rev. Mod. Phys. 20 (1948) 367. R.P. Feynman, Phys. Rev. 84 (1951) 108. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965. The idea of using the classical action in quantum mechanics was first proposed by Dirac in P.A.M. Dirac, Phys. Z. Sowietunion 3 (1933) 64 (reprinted in: J. Schwinger, Quantum Electrodynamics, Dover, New York, 1958).
    • (1951) Phys. Rev. , vol.84 , pp. 108
    • Feynman, R.P.1
  • 4
    • 34547361024 scopus 로고
    • McGraw-Hill, New York
    • R.P. Feynman, Rev. Mod. Phys. 20 (1948) 367. R.P. Feynman, Phys. Rev. 84 (1951) 108. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965. The idea of using the classical action in quantum mechanics was first proposed by Dirac in P.A.M. Dirac, Phys. Z. Sowietunion 3 (1933) 64 (reprinted in: J. Schwinger, Quantum Electrodynamics, Dover, New York, 1958).
    • (1965) Quantum Mechanics and Path Integrals
    • Feynman, R.P.1    Hibbs, A.R.2
  • 5
    • 34547361024 scopus 로고
    • The idea of using the classical action in quantum mechanics was first proposed by Dirac in (reprinted in: (reprinted in: J. Schwinger, Quantum Electrodynamics, Dover, New York, 1958)
    • R.P. Feynman, Rev. Mod. Phys. 20 (1948) 367. R.P. Feynman, Phys. Rev. 84 (1951) 108. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965. The idea of using the classical action in quantum mechanics was first proposed by Dirac in P.A.M. Dirac, Phys. Z. Sowietunion 3 (1933) 64 (reprinted in: J. Schwinger, Quantum Electrodynamics, Dover, New York, 1958).
    • (1933) Phys. Z. Sowietunion , vol.3 , pp. 64
    • Dirac, P.A.M.1
  • 15
    • 0001988542 scopus 로고
    • I.M. Singer, Commun. Math. Phys. 60 (1978) 7; M.F. Atiyah, J.D.S. Jones, Commun. Math. Phys. 61 (1978) 97.
    • (1978) Commun. Math. Phys. , vol.60 , pp. 7
    • Singer, I.M.1
  • 17
    • 0000866791 scopus 로고
    • O. Babelon, C.-M. Viallet, Phys. Lett. B 85 (1979) 246; O. Babelon, C.-M. Viallet, Commun. Math. Phys. 81 (1981) 515; M. Daniel, C.-M. Viallet, Rev. Mod. Phys. 52 (1980) 175.
    • (1979) Phys. Lett. B , vol.85 , pp. 246
    • Babelon, O.1    Viallet, C.-M.2
  • 18
    • 0001000107 scopus 로고
    • O. Babelon, C.-M. Viallet, Phys. Lett. B 85 (1979) 246; O. Babelon, C.-M. Viallet, Commun. Math. Phys. 81 (1981) 515; M. Daniel, C.-M. Viallet, Rev. Mod. Phys. 52 (1980) 175.
    • (1981) Commun. Math. Phys. , vol.81 , pp. 515
    • Babelon, O.1    Viallet, C.-M.2
  • 19
    • 0001403915 scopus 로고
    • O. Babelon, C.-M. Viallet, Phys. Lett. B 85 (1979) 246; O. Babelon, C.-M. Viallet, Commun. Math. Phys. 81 (1981) 515; M. Daniel, C.-M. Viallet, Rev. Mod. Phys. 52 (1980) 175.
    • (1980) Rev. Mod. Phys. , vol.52 , pp. 175
    • Daniel, M.1    Viallet, C.-M.2
  • 20
    • 4243542502 scopus 로고
    • J.R. Klauder, E. Aslaksen, Phys. Rev. D 2 (1970) 272; J.R. Klauder, in: J.-P. Antoine, E. Tirapequi (Eds.), Functional Integration, Plenum Pub. Corp., New York, 1980.
    • (1970) Phys. Rev. D , vol.2 , pp. 272
    • Klauder, J.R.1    Aslaksen, E.2
  • 21
    • 4243542502 scopus 로고
    • in: J.-P. Antoine, E. Tirapequi (Eds.), Plenum Pub. Corp., New York
    • J.R. Klauder, E. Aslaksen, Phys. Rev. D 2 (1970) 272; J.R. Klauder, in: J.-P. Antoine, E. Tirapequi (Eds.), Functional Integration, Plenum Pub. Corp., New York, 1980.
    • (1980) Functional Integration
    • Klauder, J.R.1
  • 31
    • 17044403515 scopus 로고
    • K. Nishijima, Nucl. Phys. B 328 (1984) 601; M. Spiegelglas, Nucl. Phys. B 283 (1987) 205; W. Kalan, J.W. van Holten, Nucl. Phys. B 361 (1991) 471.
    • (1984) Nucl. Phys. B , vol.328 , pp. 601
    • Nishijima, K.1
  • 32
    • 0000657362 scopus 로고
    • K. Nishijima, Nucl. Phys. B 328 (1984) 601; M. Spiegelglas, Nucl. Phys. B 283 (1987) 205; W. Kalan, J.W. van Holten, Nucl. Phys. B 361 (1991) 471.
    • (1987) Nucl. Phys. B , vol.283 , pp. 205
    • Spiegelglas, M.1
  • 33
    • 17044403515 scopus 로고
    • K. Nishijima, Nucl. Phys. B 328 (1984) 601; M. Spiegelglas, Nucl. Phys. B 283 (1987) 205; W. Kalan, J.W. van Holten, Nucl. Phys. B 361 (1991) 471.
    • (1991) Nucl. Phys. B , vol.361 , pp. 471
    • Kalan, W.1    Van Holten, J.W.2
  • 38
    • 0000287061 scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1979) Prog. Theor. Phys. , vol.61 , pp. 627
    • Fujikawa, K.1
  • 39
    • 0002365925 scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1979) Nucl. Phys. B , vol.157 , pp. 37
    • Hirschfeld, P.1
  • 40
    • 0001031189 scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1986) Nucl. Phys. B , vol.266 , pp. 357
    • Carson, L.J.1
  • 41
    • 0002339184 scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1990) Lett. Math. Phys. , vol.19 , pp. 249
    • Kanno, H.1
  • 42
    • 0011613033 scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1991) Ann. Phys. , vol.209 , pp. 231
    • Yabuki, H.1
  • 43
    • 0030579684 scopus 로고    scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1996) Nucl. Phys. B , vol.462 , pp. 571
    • Becchi, C.1    Imbimbo, C.2
  • 44
    • 3042876494 scopus 로고    scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1996) Phys. Rev. D , vol.54 , pp. 7825
    • Baulieu, L.1    Rosenberg, A.2    Schaden, M.3
  • 45
    • 0031564678 scopus 로고    scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1997) Commun. Math. Phys. , vol.185 , pp. 723
    • Zucchini, R.1
  • 46
    • 0346705138 scopus 로고    scopus 로고
    • K. Fujikawa, Prog. Theor. Phys. 61 (1979) 627; P. Hirschfeld, Nucl. Phys. B 157 (1979) 37; L.J. Carson, Nucl. Phys. B 266 (1986) 357; H. Kanno, Lett. Math. Phys. 19 (1990) 249; H. Yabuki, Ann. Phys. 209 (1991) 231; C. Becchi, C. Imbimbo, Nucl. Phys. B 462 (1996) 571; L. Baulieu, A. Rosenberg, M. Schaden, Phys. Rev. D 54 (1996) 7825; R. Zucchini, Commun. Math. Phys. 185 (1997) 723; M. Testa, Phys. Lett. B 429 (1998) 349.
    • (1998) Phys. Lett. B , vol.429 , pp. 349
    • Testa, M.1
  • 49
    • 0000290463 scopus 로고
    • Compact lie groups and their representations
    • American Mathematical Society, Providence, RI
    • D.P. Zhelobenko, Compact Lie Groups and Their Representations, Translations of Mathematical Monographs, Vol. 40, American Mathematical Society, Providence, RI, 1973.
    • (1973) Translations of Mathematical Monographs , vol.40
    • Zhelobenko, D.P.1
  • 50
    • 0002367569 scopus 로고
    • Quarks, leptons and gauge fields
    • Singapore
    • K. Huang, Quarks, Leptons and Gauge Fields, World Scientific, Singapore, 1982.
    • (1982) World Scientific
    • Huang, K.1
  • 89
    • 0003366306 scopus 로고
    • Phase space structure in gauge theories
    • JINR Publ. Dep., Dubna (in Russian)
    • S.V. Shabanov, Phase Space Structure in Gauge Theories, JINR lectures for young scientists, Vol. 54, P2-89-533, JINR Publ. Dep., Dubna, 1989 (in Russian).
    • (1989) JINR Lectures for Young Scientists , vol.54 , pp. 289-533
    • Shabanov, S.V.1
  • 94
    • 0003749547 scopus 로고
    • in: S. Hawking, W. Israel (Eds.) Cambridge Univ. Press, Cambridge
    • B. DeWitt, in: S. Hawking, W. Israel (Eds.), General Relativity: An Einstein Centenary Survey, Cambridge Univ. Press, Cambridge, 1979; K. Kuchar, Phys. Rev. D 34 (1986) 3044.
    • (1979) General Relativity: An Einstein Centenary Survey
    • DeWitt, B.1
  • 95
    • 0001421866 scopus 로고
    • B. DeWitt, in: S. Hawking, W. Israel (Eds.), General Relativity: An Einstein Centenary Survey, Cambridge Univ. Press, Cambridge, 1979; K. Kuchar, Phys. Rev. D 34 (1986) 3044.
    • (1986) Phys. Rev. D , vol.34 , pp. 3044
    • Kuchar, K.1
  • 108
    • 0009339752 scopus 로고
    • P.A.M. Dirac, Can. J. Math. 2 (1950) 129; 3 (1951) 1.
    • (1951) Can. J. Math. , vol.3 , pp. 1
  • 120
    • 0003574632 scopus 로고    scopus 로고
    • Confinement, duality, and nonperturbative aspects of QCD
    • in: P. van Baal (Ed.), Plenum Press, New York
    • P. van Baal, in: P. van Baal (Ed.), Confinement, Duality, and Nonperturbative Aspects of QCD, NATO ASI Series, Vol. B 368, Plenum Press, New York, 1998.
    • (1998) NATO ASI Series , vol.B , pp. 368
    • Van Baal, P.1
  • 125
  • 133
    • 0004048496 scopus 로고
    • An Introduction, Springer, Berlin
    • L.S. Schulmann, Techniques and Applications of Path Integration, Wiley, New York, 1981; G. Roepsdorff, Path Integral Approach to Quantum Physics. An Introduction, Springer, Berlin, 1994.
    • (1994) Path Integral Approach to Quantum Physics.
    • Roepsdorff, G.1
  • 136
  • 147
    • 0002339190 scopus 로고
    • 1239
    • B. de Witt, Phys. Rev. 162 (1967) 1192, 1239.
    • (1967) Phys. Rev. , vol.162 , pp. 1192
    • De Witt, B.1
  • 151
    • 0004673714 scopus 로고
    • JINR preprint, E2-89-687, Dubna (unpublished)
    • S.V. Shabanov, Path integral in holomorphic representation without gauge fixation, JINR preprint, E2-89-687, Dubna, 1989 (unpublished); see a revised version in: V.S. Yarunin, M.A. Smondyrev (Eds.), The Proceedings of "Path Integrals'96", JINR Publ. Dept., Dubna, 1996, p. 133.
    • (1989) Path Integral in Holomorphic Representation Without Gauge Fixation
    • Shabanov, S.V.1
  • 152
    • 0002347309 scopus 로고    scopus 로고
    • see a revised version in: (Eds.) JINR Publ. Dept., Dubna
    • S.V. Shabanov, Path integral in holomorphic representation without gauge fixation, JINR preprint, E2-89-687, Dubna, 1989 (unpublished); see a revised version in: V.S. Yarunin, M.A. Smondyrev (Eds.), The Proceedings of "Path Integrals'96", JINR Publ. Dept., Dubna, 1996, p. 133.
    • (1996) The Proceedings of "Path Integrals'96" , pp. 133
    • Yarunin, V.S.1    Smondyrev, M.A.2
  • 161
    • 0004098158 scopus 로고
    • in: A.A. Kirillov (Ed.) D. Reidel Publ. Co., Dordrecht, Holland
    • F.A. Berezin, in: A.A. Kirillov (Ed.), Introduction to Superanalysis, D. Reidel Publ. Co., Dordrecht, Holland, 1987.
    • (1987) Introduction to Superanalysis
    • Berezin, F.A.1
  • 162
    • 0004171988 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • B. DeWitt, Supermanifolds, Cambridge Univ. Press, Cambridge, 1984.
    • (1984) Supermanifolds
    • DeWitt, B.1
  • 168
    • 0002268330 scopus 로고
    • Lectures on quantization of gauge theories by the path integral method
    • in: E.N. Gazis, G. Koutsoumbas, N.D. Tracas, G. Zoupanos (Eds.) Corfu, September 1992, National Technical University, Athens
    • S.V. Shabanov, Lectures on Quantization of Gauge Theories by the Path Integral Method, in: E.N. Gazis, G. Koutsoumbas, N.D. Tracas, G. Zoupanos (Eds.), The Proceedings of 4th Hellenic School on Elementary Particle Physics, vol. II, Corfu, September 1992, National Technical University, Athens, 1994, p. 272.
    • (1994) The Proceedings of 4th Hellenic School on Elementary Particle Physics , vol.2 , pp. 272
    • Shabanov, S.V.1
  • 173
    • 9744226080 scopus 로고
    • S.W. Howking, Phys. Lett. B 195 (1987); Phys. Rev. D 37 (1988) 904.
    • (1988) Phys. Rev. D , vol.37 , pp. 904
  • 176
    • 0010184718 scopus 로고
    • S. Coleman, Nucl. Phys. B 307 (1988) 867; 310 (1988) 643.
    • (1988) Nucl. Phys. B , vol.310 , pp. 643
  • 180
    • 36049055961 scopus 로고
    • B. DeWitt, Phys. Rev. D 160 (1967) 1113; C. Isham, J.E. Nelson, Phys. Rev. D 10 (1974) 3226; W.E. Blyth, C. Isham, Phys. Rev. D 11 (1975) 768.
    • (1967) Phys. Rev. D , vol.160 , pp. 1113
    • DeWitt, B.1
  • 181
    • 0000651114 scopus 로고
    • B. DeWitt, Phys. Rev. D 160 (1967) 1113; C. Isham, J.E. Nelson, Phys. Rev. D 10 (1974) 3226; W.E. Blyth, C. Isham, Phys. Rev. D 11 (1975) 768.
    • (1974) Phys. Rev. D , vol.10 , pp. 3226
    • Isham, C.1    Nelson, J.E.2
  • 182
    • 0000109697 scopus 로고
    • B. DeWitt, Phys. Rev. D 160 (1967) 1113; C. Isham, J.E. Nelson, Phys. Rev. D 10 (1974) 3226; W.E. Blyth, C. Isham, Phys. Rev. D 11 (1975) 768.
    • (1975) Phys. Rev. D , vol.11 , pp. 768
    • Blyth, W.E.1    Isham, C.2
  • 194
    • 0002346183 scopus 로고
    • Translation: Plenum Press, New York
    • M.A. Semenov-Tyan-Shanskii, V.A. Franke, Zapiski Nauch. Sem. Len. Otdel. Mat. Inst. im. V.A. Steklov AN SSSR, 120 (1982) 159; Translation: Plenum Press, New York, 1986, p. 999.
    • (1986) , pp. 999
  • 201
    • 0002346185 scopus 로고
    • Dissertationes Mathematicae, Warsaw, CCL
    • W. Kondracki, J.S. Rogulski, Dissertationes Mathematicae, Warsaw, CCL (1986) 1.
    • (1986) , pp. 1
    • Kondracki, W.1    Rogulski, J.S.2
  • 243
    • 0003667496 scopus 로고
    • Quantization of relativistic systems with constraints: Equivalence of canonical and covariant formalisms in quantum theory of gravitational field
    • E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints: equivalence of canonical and covariant formalisms in quantum theory of gravitational field, CERN report TH-2332, 1977; I.A. Batalin, G.A. Vilkovisky, Phys. Lett. B 69 (1977) 309; L. Baulieu, Phys. Rep. 129 (1985) 3.
    • (1977) CERN Report TH-2332
    • Fradkin, E.S.1    Vilkovisky, G.A.2
  • 244
    • 0040969973 scopus 로고
    • E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints: equivalence of canonical and covariant formalisms in quantum theory of gravitational field, CERN report TH-2332, 1977; I.A. Batalin, G.A. Vilkovisky, Phys. Lett. B 69 (1977) 309; L. Baulieu, Phys. Rep. 129 (1985) 3.
    • (1977) Phys. Lett. B , vol.69 , pp. 309
    • Batalin, I.A.1    Vilkovisky, G.A.2
  • 245
    • 0002355668 scopus 로고
    • E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints: equivalence of canonical and covariant formalisms in quantum theory of gravitational field, CERN report TH-2332, 1977; I.A. Batalin, G.A. Vilkovisky, Phys. Lett. B 69 (1977) 309; L. Baulieu, Phys. Rep. 129 (1985) 3.
    • (1985) Phys. Rep. , vol.129 , pp. 3
    • Baulieu, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.