Coherent states and the quantization of (1 + 1)-dimensional Yang-Mills theory

Reviews in Mathematical Physics

Volumn 13, Issue 10, 2001, Pages 1281-1305

  Hall, Brian C ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035602438     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X0100096X     Document Type: Article

References (44)

1. B. K. Driver and B. C. Hall, Comm. Math. Phys. 201 (1999) 249.
2. B. C. Hall, J. Funct. Anal. 122 (1994) 103.
3. B. C. Hall, Bull. (N.S.) Amer. Math. Soc. 38 (2001) 43.
4. K. Gawȩdzki, Phys. Rev. D26 (1982) 3593.
5. L. Gross and P. Malliavin, "Hall's transform and the Segal-Bargmann map", pp. 73-116 in Itô's Stochastic Calculus and Probability Theory, eds. M. Fukushima et al., Springer-Verlag, New York/Berlin, 1996.
6. K. K. Wren, Nucl. Phys. B521 (1998) 472.
7. N. P. Landsman, J. Geom. Phys. 15 (1995) 285.
8. N. P. Landsman and K. K. Wren, Nucl. Phys. B502 (1997) 537.
9. N. P. Landsman, Mathematical Topics between Classical and Quantum Mechanics, Springer-Verlag, New York/Berlin, 1998.
10. S. Rajeev, Phys. Lett. B212 (1988) 203.
11. J. Dimock, Rev. Math. Phys. 8 (1996) 85.
12. L. Gross, J. Funct. Anal. 112 (1993) 373.
13. B. K. Driver and B. C. Hall, "The energy representation has non-zero fixed vectors", pp. 143-155 in Stochastic Processes, Physicsand Geometry: New Interplays. II: A Volume in Honor of Sergio Albeverio, eds. F. Gesztesy et al., Amer. Math. Soc., Providence, RI, 2000.
14. V. Bargmann, Comm. Pure Appl. Math. 14 (1961) 187.
15. I. E. Segal, "Mathematical problems of relativistic physics", pp. 73-84 in Lectures in Applied Mathematics. Proceedings of the Summer Seminar, Boulder, Colorado, 1960, Vol. II, ed. M. Kac, American Math. Soc, Providence, R.I., 1963.
16. I. E. Segal, Illinois J. Math. 6 (1962) 500.
17. I. E. Segal, "The complex wave representation of the free Boson field", pp. 321-343 in Topics in functional analysis. Essays dedicated to M. G. Krein on the occasion of his 70th birthday, eds. I. Gohberg and M. Kac, Advances in Mathematics Supplementary Studies, Vol. 3, Academic Press, New York, 1978.
18. J. Baez, I. E. Segal and Z. Zhou, Introduction to Algebraic and Constructive Quantum Field Theory, Princeton Univ. Press, Princeton, NJ, 1992.
19. B. C. Hall, "Holomorphic methods in analysis and mathematical physics", pp. 1-59 in First Summer School in Analysis and Mathematical Physics, eds. S. Pérez-Esteva and C. Villegas-Blas, Contemp. Math., Vol. 260, Amer. Math. Soc., Providence, R.I., 2000.
20. B. C. Hall, Can. J. Math. 51 (1999) 816.
21. A. N. Sengupta, "The two-parameter Segal-Bargmann transform", (preprint).
22. B. C. Hall and A. N. Sengupta, J. Funct. Anal. 152 (1998) 220.
23. J. R. Klauder, Ann. Physics 254 (1997) 419.
24. J. R. Klauder, Nuclear Phys. B547 (1999) 397.
25. J. Govaerts and J. R. Klauder, Ann. Physics 274 (1999) 251.
26. J. R. Klauder and B.-S. Skagerstam (Eds.), Coherent States. Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985.
27. A. Perelomov, Generalized Coherent States and Their Applications, Springer-Verlag, New York/Berlin, 1986.
28. B. C. Hall, Comm. Math. Phys. 184 (1997) 233.
29. B. C. Hall, "Quantum mechanics in phase space", pp. 47-62 in Perspectives on Quantization, eds. L. Coburn and M. Rieffel, Contemp. Math., Vol. 214, Amer. Math. Soc., Providence, RI, 1998.
30. F. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry, Mathematical Notes 31, Princeton Univ. Press, Princeton, N.J., 1984.
31. D. Mumford, J. Fogarty and F. Kirwan, Geometric Invariant Theory, Third edition, Ergebnisse der Mathematik und ihrer Grenzgebiete 34, Springer-Verlag, New York/Berlin, 1994.
32. V. Guillemin and M. Stenzel, J. Differential Geom. 34 (1991) 561.
33. V. Guillemin and M. Stenzel, J. Differential Geom. 35 (1992) 627.
34. L. Lempert and R. Szoke, Math. Ann. 290 (1991) 689.
35. R. Szoke, Math. Ann. 291 (1991) 409.
36. R. M. Aguilar, "Symplectic reduction and new global unbounded solutions of the homogeneous complex Monge-Ampère equation", (preprint).
37. B. C. Hall, "Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type", (preprint), [xxx.lanl.gov, quant-ph/0012105].
38. N. J. M. Woodhouse, Geometric Quantization, Second edition, Oxford Univ. Press, New York, 1992.
39. V. Guillemin and S. Sternberg, Invent. Math. 67 (1982) 515.
40. D. Freed, personal communication.
41. L. Gross, "Abstract Wiener spaces", pp. 31-42 in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, Univ. of California Press, 1967.
42. H.-H. Kuo, Guassian Measures in Banach Spaces, Lecture Notes in Mathematics, Vol. 463, Springer-Verlag, New York/Berlin, 1975.
43. J. Glimm and A. Jaffe, Quantum Physics. A Functional Integral Point of View, Second edition, Springer-Verlag, New York/Berlin, 1987.
44. R. Sjamaar, Bull. (N.S.) Amer. Math. Soc. 33 (1996) 327.