Diffeomorphism groups and current algebras: Configuration space analysis in quantum theory

Reviews in Mathematical Physics

Volumn 11, Issue 1, 1999, Pages 1-23

  Albeverio, S ^a   Kondratiev, Yu G ^b,c   Rockner M ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b BIELEFELD UNIVERSITY   (Germany)

^c INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033484085     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X99000027     Document Type: Article

References (48)

1. S. Albeverio, Yu. L. Daletsky, Yu. G. Kondratiev and L. Streit, "Non-Gaussian infinite dimensional analysis", J. Func. Anal. 136 (1996) 1-41.
2. S. Albeverio and R. Høegh-Krohn, "Dirichlet forms and diffusion processes on rigged Hilbert spaces". Zeitsh. Wahr. u. verw. Gebiete 40 (1977) 242-272.
3. S. Albeverio, R. Høegh-Krohn and L. Streit, "Energy forms, Hamiltonians, and distorted Brownian paths", J. Math. Phys. 18 (1977) 907-917.
4. S. Albeverio, R. Høegh-Krohn, J. Marion, D. Testard and B. Torresani, Noncommutative Distributions-Unitary Representations of Gauge Groups and Algebras, M. Dekker, New York, 1993.
5. S. Albeverio, Yu. G. Kondratiev and M. Röckner, "Differential geometry of Poisson spaces", C. R. Acad. Sci. Paris 323 (1996) 1129-1134.
6. S. Albeverio, Yu. G. Kondratiev and M. Röckner, "Canonical Dirichlet operator and distorted Brownian motion on Poisson spaces", C. R. Acad. Sci. Paris 323 (1996) 1179-1184.
7. S. Albeverio, Yu. G. Kondratiev and M. Röckner, Analysis and Geometry on Configuration Spaces, SFB-343 Preprint 97-050, Bielefeld Univ., 1997.
8. S. Albeverio, Yu. G. Kondratiev and M. Röckner, "Analysis and geometry on configuration spaces: Part II. The Gibbsian case", in preparation, 1997.
9. S. Albeverio, Yu. G. Kondratiev, Z.-M. Ma and M. Röckner, "Stochastic dynamics for quantum continuous system", in preparation, 1997.
10. H. Araki, "Hamiltonian formalism and the canonical commutation relations in quantum field theory", J. Math. Phys. 1 (1960) 492-504.
11. Yu. M. Berezansky and Yu. G. Kondratiev, Spectral Methods in Infinite Dimensional Analysis, Kluwer Academic Publishers, Holland, 1995.
12. F. Coester and R. Haag, "Representation of states in a field theory with canonical variables", Phys. Rev. 117 (1960) 1137-1145.
13. J. L. Doob, Stochastic Processes, New York-London, 1953.
14. R. Dashen and D. H. Sharp, "Currents as coordinates for hadrons", Phys. Rev. 165 (1968) 1857-1867.
15. R. L. Dobrushin, "On Poisson distribution of particles in space", Ukr. Math. J. 8 (1956) 127-134.
16. R. L. Dobrushin, "Gibbs random fields for particles withoud hard core", Theor. Math. Phys. 4 (1970) 101-118.
17. H. O. Georgii, Canonical Gibbs Measures, LNM 760, Springer-Verlag, 1979.
18. I. M. Gelfand and N. Ya. Vilenkin, Some Applications of Harmonic Analysis. Rigged Hilbert Spaces, Academic Press, 1964.
19. J. Glimm and A. Jaffe, Quantum Physics: A Functional Integral Point of View, Springer-Verlag, 1981.
20. G. Goldin, K. J. Grodnik, R. T. Powers and D. H. Sharp, "Nonrelativistic current algebra in the N/V limit", J. Math. Phys. 15 (1974) 88-100.
21. G. Goldin and D. H. Sharp, 1969 Battelle Rencontres: Group Representations, Lect. Notes Phys. 6 ed. V. Bargmann, 1970.
22. G. Goldin and D. H. Sharp, "The diffeomorhism group approach to anyons", Int. J. Modern Phys. 5 (1991) 2625-2640.
23. G. Goldin and D. H. Sharp, "Diffeomorphism groups, anyon fields, and q commutators", Phys. Rev. Lett. 1996 (1996) 1183-1187.
24. G. Goldin, R. Menikoff and D. H. Sharp, "Quantum vortex configurations in three dimensions," Phys. Rev. Lett. 67 (1991) 3499-3504.
25. G. Goldin and U. Moschella, "Quantum phase transitions from a new class of representations of a diffeomorphism group", J. Phys. A: Math. Gen. 28 (1995) L475-L481.
26. G. Goldin and U. Moschella, "Diffeomorphism groups, quasi-invariant measures, and infinite quantum systems", preprint.
27. J. Grodnik and D. H. Sharp, Phys. Rev. D 1 (1970) 1546.
28. K. Hepp, Théorie de la Renormalisation, Springer-Verlag, 1969.
29. I. W. Herbst, "On canonical quantum field theories", J. Math. Phys. 17 (1976) 1210-1221.
30. Y. Ito and I. Kubo, "Calculus on Gaussian and Poisson white noises", Nagoya Math. J., 111 (1988) 41-84.
31. n, n ≥ 2", Math. USSR-Sb. 27 (1975) 55-71.
32. R. S. Ismagilov, Representations of Infinite-Dimensional Groups, AMS, Providence, Rhode Island, 1996.
33. K. Ito, "Spectral type of the shift transformation of differential processes with stationary increments", TRAMS 81 (1956) 253-263.
34. Yu. G. Kondratiev, E. W. Lytvynov, A. L. Rebenko, M. Röckner and G. V. Schepan'uk, "Euclidean Gibbs states for continuous quantum systems with Boltz-mann statistics", in preparation, 1997.
35. Yu. G. Kondratiev, L. Silva and L. Streit, Generalized Appell systems, Methods Funct. Anal. and Topology 3 (1997), 28-61.
36. A. Martin-Löf, "Limit theorems or the motion of a Poisson system of independent Markovian particles with high density", Z. Wahrsch. verw, Gebiete 34 (1976) 205-223.
37. R. Menikoff, "The Hamiltonian and generating functional for a nonrelativistic local current algebra", J. Math. Phys, 15 (1974) 1138-1152.
38. R. Menikoff, "Generating functionals determinig representations of a nonrelativistic local current algebra in the N/V limit", J. Math. Phys. 15 (1974) 1394-1408.
39. R. Menikoff and D. H. Sharp, "Representations of a local current algebra: their dynamical determination", J. Math. Phys. 16 (1975) 2341-2352.
40. H. Osada, "Dirichlet form approach to infinite-dimensional Wiener process with singular interactions". Commun. Math. Phys.. 176 (1996) 117-131.
41. C. J. Preston, Random Fields, LNM 534, Springer, 1976.
42. D. Ruelle, "Superstable interactions in classical statistical mechanics", Commun. Math. Phys. 18 (1970) 127-159.
43. 2 Euclidean (Quantum) Field Theory, Princeton University Press, 1974.
44. A. V. Skorokhod, "On the differentiability of measures which corresponds to stochastic prosesses I. Processes with independent increments", Theria Verojat. Primen. 2 (1957) 418-444.
45. T. Shiga and Y. Takahashi, "Ergodic properties of the equilibrium process associated with infinitely many Markovian particles", Publ. RIMS, Kyoto Univ. 9 (1974) 505-516.
46. Y. Takahashi, "Absolute continuity of Poisson random fields", Publ. RIMS Kyoto Univ. 26 (1990) 629-647.
47. A. M. Vershik, I. M. Gelfand and M. I. Graev, "Representations of the group of diffeomorphisms", Russ. Math. Surv. 30 (1975) 1-50.
48. M. W. Yoshida, "Construction of infinite-dimensional interacting diffusion processes through Dirichet forms". Probab. Th. Rel. Fields 106 (1996) 265-297.