The symplectic geometry of a parametrized scalar field on a curved background

Journal of Mathematical Physics

Volumn 37, Issue 7, 1996, Pages 3505-3521

  Hajicek P ^a   Isham, C J ^b  

^a UNIVERSITY OF BERN   (Switzerland)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030547595     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531578     Document Type: Article

References (21)

1. B. S. DeWitt, Phys. Rep. 19C, 295-357 (1975).
2. C. J. Isham, "Quantum field theory in curved space-time, an overview," in Proceedings of the 8th Texas Symposium on Relativistic Astrophysics, edited by M. Papagiannis (New York Academy of Sciences, New York, 1977), pp. 114-157.
3. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).
4. P. A. M. Dirac, Can. J. Math. 3, 1 (1951).
5. K. V. Kuchař, J. Math. Phys. 17, 777 (1976).
6. K. V. Kuchař, J. Math. Phys. 17, 801 (1976).
7. C. J. Isham and K. V. Kuchař, Ann. Phys. 164, 288 (1985).
8. K. V. Kuchař, "Canonical methods of quantization," in Quantum Gravity 2: A Second Oxford Symposium, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Clarendon University, Oxford, 1981), pp. 329-374.
9. P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949).
10. P. Hájíček, J. Math. Phys. 36, 4612 (1995).
11. C. J. Isham, "Topological and global aspects of quantum theory," in Relativity, Groups and Topology II, edited by R. Stora and B. S. DeWitt (North-Holland, Amsterdam, 1984), pp. 1061-1290.
12. A. Ashtekar, Lectures on Non-Perturbative Quantum Gravity (World Scientific, Singapore, 1991).
13. P. R. Chernov and J. E. Marsden, Properties of Infinite Dimensional Hamiltonian Systems, Lecture Notes in Mathematics, edited by A. Dold and B. Eckmann (Springer-Verlag, Berlin, 1974).
14. P. Hájíček and C. J. Isham, "Perennials and the group-theoretical quantization of a parametrized scalar field on a curved background," Imperial College Report No. IMPERIAL/TP/95-96/2 (1995) gr-qc/9510034.
15. A. E. Fischer and J. E. Marsden, "The initial value problem and the dynamical formulation of general relativity," in General Relativity. An Einstein Centenary Review, edited by S. W. Hawking and W. Israel (Cambridge University, Cambridge, 1979), pp. 138-211.
16. S. W. Hawking and J. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University, Cambridge, 1973), Chap. 7.
17. I. M. Gel'fand and N. J. Vilenkin, Generalized Functions IV (Academic, New York, 1964).
18. K. V. Kuchař, "Time and interpretations of quantum gravity," in Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics (World Scientific, Singapore, 1992), pp. 211-314.
19. J. Eells, "On the Geometry of Function Spaces," in Symposium de Topoloqia Algebrica, Mexico (1958), pp. 303-307.
20. J. E. Marsden, D. G. Ebin, and A. E. Fischer, "Diffeomorphism Groups, Hydrodynamics and Relativity," in Proceedings of the 13th Biennial Seminar of the Canadian Mathematical Congress, edited by J. R. Vanstone (Canadian Mathematical Congress, Montreal, 1972), pp. 135-279.
21. S. Lang, Differential Manifolds (Addison-Wesley, Reading, 1972).