Coordinate-free quantization of second-class constraints

Nuclear Physics B

Volumn 511, Issue 3, 1998, Pages 713-736

  Klauder, John R ^a   Shabanov, Sergei V ^b,c  

^a UNIVERSITY OF FLORIDA   (United States)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

^c JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032498459     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00678-0     Document Type: Article

References (24)

1. [1] P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, NY, 1964).
2. [2] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 2nd Ed. (Clarendon Press, Oxford, 1993).
3. [3] J.R. Klauder, Ann. Phys. 188 (1988) 120.
4. [4] J.R. Klauder and S.V. Shabanov, Phys. Lett. B 398 (1997) 116 (hep-th/9608027).
5. [5] P.A.M. Dirac, The Principles of Quantum Mechanics, 3rd Ed. (Oxford University Press, Oxford, 1947) p. 114.
6. [6] For a review of basic principles of the deformation quantization see, e.g., A. Weinstein, in Séminaire BOURBAKI, 46ème année, 1993-94, no 789; Quantization of Poisson manifolds is discussed in M. Kontsevich, Lectures on deformation theory, preprint, University of California, Berkeley, Spring 1995; A.A. Voronov, Quantizing Poisson manifolds, q-alg/9701017.
7. [6] For a review of basic principles of the deformation quantization see, e.g., A. Weinstein, in Séminaire BOURBAKI, 46ème année, 1993-94, no 789; Quantization of Poisson manifolds is discussed in M. Kontsevich, Lectures on deformation theory, preprint, University of California, Berkeley, Spring 1995; A.A. Voronov, Quantizing Poisson manifolds, q-alg/9701017.
8. [6] For a review of basic principles of the deformation quantization see, e.g., A. Weinstein, in Séminaire BOURBAKI, 46ème année, 1993-94, no 789; Quantization of Poisson manifolds is discussed in M. Kontsevich, Lectures on deformation theory, preprint, University of California, Berkeley, Spring 1995; A.A. Voronov, Quantizing Poisson manifolds, q-alg/9701017.
9. [7] N. Ogawa, K. Fujii, N. Chepilko and A. Kobushkin, Prog. Theor. Phys. 85 (1991) 1189.
10. [8] B.S. De Witt, Rev. Mod. Phys. 29 (1957) 377; K.S. Cheng, J. Math. Phys. 13 (1972) 1723; H. Dekker, Physica A 103 (1980) 586.
11. [8] B.S. De Witt, Rev. Mod. Phys. 29 (1957) 377; K.S. Cheng, J. Math. Phys. 13 (1972) 1723; H. Dekker, Physica A 103 (1980) 586.
12. [8] B.S. De Witt, Rev. Mod. Phys. 29 (1957) 377; K.S. Cheng, J. Math. Phys. 13 (1972) 1723; H. Dekker, Physica A 103 (1980) 586.
13. [9] H. Kleinert and S.V. Shabanov, Phys. Lett. A 232 (1997) 327.
14. [10] R.C.T. da Costa, Phys. Rev. 23 (1981) 1982; N. Ogawa, Prog. Theor. Phys. 87 (1992) 513.
15. [10] R.C.T. da Costa, Phys. Rev. 23 (1981) 1982; N. Ogawa, Prog. Theor. Phys. 87 (1992) 513.
16. [11] L.D. Faddeev and S.L. Shatashvili, Phys. Lett. B 167 (1986) 225; I.A. Batalin and E.S. Fradkin, Nucl. Phys. B 279 (1987) 514; E.Sh. Egorian and R.P. Manvelyan, preprint YEPHI-1056(19)-88, Yerevan, 1988; I.A. Batalin, E.S. Fradkin and T.E. Fradkina, Nucl.Phys. B 314 (1989) 158.
17. [11] L.D. Faddeev and S.L. Shatashvili, Phys. Lett. B 167 (1986) 225; I.A. Batalin and E.S. Fradkin, Nucl. Phys. B 279 (1987) 514; E.Sh. Egorian and R.P. Manvelyan, preprint YEPHI-1056(19)-88, Yerevan, 1988; I.A. Batalin, E.S. Fradkin and T.E. Fradkina, Nucl.Phys. B 314 (1989) 158.
18. [11] L.D. Faddeev and S.L. Shatashvili, Phys. Lett. B 167 (1986) 225; I.A. Batalin and E.S. Fradkin, Nucl. Phys. B 279 (1987) 514; E.Sh. Egorian and R.P. Manvelyan, preprint YEPHI-1056(19)-88, Yerevan, 1988; I.A. Batalin, E.S. Fradkin and T.E. Fradkina, Nucl.Phys. B 314 (1989) 158.
19. [11] L.D. Faddeev and S.L. Shatashvili, Phys. Lett. B 167 (1986) 225; I.A. Batalin and E.S. Fradkin, Nucl. Phys. B 279 (1987) 514; E.Sh. Egorian and R.P. Manvelyan, preprint YEPHI-1056(19)-88, Yerevan, 1988; I.A. Batalin, E.S. Fradkin and T.E. Fradkina, Nucl.Phys. B 314 (1989) 158.
20. [12] I.A. Batalin and I.V. Tyutin, Int. J. Mod. Phys. A 6 (1991) 3255.
21. [13] L.V. Prokhorov and S.V. Shabanov, Hamiltonian Dynamics of Gauge Systems, St.-Petersburg University Press, St.-Petersburg, 1996; (Section 3.4.3) (in Russian).
22. [14] J.R. Klauder, Ann. of Phys. 254 (1997) 419; for compact gauge groups the projection method was also studied, in S.V. Shabanov, Path integral in holomorphic representation without gauge fixation, JINR preprint E2-89-687, Dubna, 1989 (unpublished) (revised version in the Proc. of Path Integrals'96, Dubna, JINR, 1996, p. 133; quant-ph/9608018).
23. [14] J.R. Klauder, Ann. of Phys. 254 (1997) 419; for compact gauge groups the projection method was also studied, in S.V. Shabanov, Path integral in holomorphic representation without gauge fixation, JINR preprint E2-89-687, Dubna, 1989 (unpublished) (revised version in the Proc. of Path Integrals'96, Dubna, JINR, 1996, p. 133; quant-ph/9608018).
24. [15] M.C. Ashworth, Coherent state approach to time reparametrization invariant systems, quant-ph/9611026.