Geometrization of statistical mechanics

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 455, Issue 1985, 1999, Pages 1683-1715

  Brody, Dorje C ^a,c   Hughston, Lane P ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b CHURCHILL COLLEGE   (United Kingdom)

^c KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Equilibrium statistical mechanics; Hubert space geometry; Projective geometry; Quantum dynamics

Indexed keywords

EID: 0041490566     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0376     Document Type: Article

References (44)

1. Anandan, J. ; Aharonov, Y. 1990 Phys. Rev. Lett. 65, 1697.
2. Ashtekar, A. ;: Schilling, T. A. 1998 In On Einstein's path (ed. A. Harvey). Berlin: Springer.
3. Bratteli, O. ; Robinson, D. W. 1979 Operator algebras and quantum statistical mechanics, vol. I. New York: Springer.
4. Bratteli, O. ; Robinson, D. W. 1981 Operator algebras and quantum statistical mechanics, vol. II. New York: Springer.
5. Brody, D. C. ; Hughston, L. P. 1996 Phys. Rev. Lett. 77, 2851.
6. Brody, D. C. ;: Hughston, L. P. 1997 Phys. Lett. A 236, 257.
7. Brody, D. C. ; Hughston, L. P. 1998a In The geometric universe: science, geometry, and the work of Roger Penrose (ed. S. A. Huggett, L. J. Mason, K. P. Tod, S. T. Tsou ; N. M. J. Woodhouse). Oxford University Press.
8. Brody, D. C. ; Hughston, L. P. 1998; Phys. Lett. A 245, 73.
9. Brody, D. C. ; Hughston, L. P. 1998c Proc. R. Soc. Land. A 454, 2445.
10. Brody, D. C. ; Hughston, L. P. 1998d J. Math. Phys. 39, 6502.
11. Brody, D. C. ; Hughston, L. P. 1999 J. Math. Phys. 40, 12.
12. Brody, D. ; Rivier, N. 1995 Phys. Rev. E 51, 1006.
13. Ellis, R. S. 1985 Entropy, large deviations, and statistical mechanics. New York and Berlin: Springer.
14. Feshbach, H. 1987 Phys. Today (November), p. 10.
15. Gibbons, G. W. 1992 J. Geom. Phys. 8, 147.
16. Gibbons, G. W. 1997 Class. Quant. Grav. 14, A155.
17. Gibbons, G. W. ; Pohle, H. J. 1993 Nucl. Phys. B 410, 117.
18. Gisin, N. 1989 Helv. Phys. Acta. 62, 363.
19. Haag, R. ; Kastler, D. 1964 J. Math. Phys. 5, 848.
20. Haag, R., Hugenholtz, N. M. ; Winnink, M. 1967 Commun. Math. Phys. 5, 215.
21. Hughston, L. P. 1995 In Tvjistor theory (ed. S. Huggett). New York: Marcel Dekker.
22. Hughston, L. P. 1996 Proc. R. Soc. Land. A 452, 953.
23. Hughston, L. P. ; Hurd, T. R. 1983 Phys. Rep. 100, 273.
24. Hughston, L. P. ; Tod, K. P. 1990 An introduction to general relativity. Cambridge University Press.
25. Kibble, T. W. B. 1978 Commun. Math. Phys. 64, 239.
26. Kibble, T. W. B. 1979 Commun. Math. Phys. 65, 189.
27. Kittel, C. 1988 Phys. Today (May), p. 93.
28. Kobayashi, S. ; Nomizu, K. 1963 Foundations of differential geometry, vol. 1. New York: Wiley.
29. Kobayashi, S. and Nomizu, K. 1969 Foundations of differential geometry, vol. 2. New York: Wiley.
30. Kubo, R. 1951 Statistical mechanics. Tokyo: Kyoritsu.
31. Kubo, R. 1957 Phys. Soc. Japan 12, 570.
32. Landsman, N. P. 1998 Mathematical topics between classical and quantum mechanics New York: Springer.
33. Mandelbrot, B. 1962 Ann. Math. Stat. 33, 1021.
34. Mandelbrot, B. 1989 Phys. Today (January), p. 71.
35. Martin, P. C. ; Schwinger, J. 1959 Phys. Rev. 115, 1342.
36. Pearle, P. 1993 Phys. Rev. A 48, 913.
37. Percival, I. 1994 Proc. R. Soc. Lond. A 447, 189.
38. Ross, S. 1996 Stochastic process. New York: Wiley.
39. Rugh, H. H. 1997 Phys. Rev. Lett. 78, 772.
40. Thompson, C. J. 1972 Mathematical statistical mechanics. Princeton University Press.
41. Tomonaga, Y. 1970 Riemannian geometry. Tokyo: Kyoritsu.
42. Weinberg, S. 1989a Phys. Rev. Lett. 62, 485.
43. Weinberg, S. 19896 Ann. Phys. 194, 336.
44. Xia, D. X. 1972 Measure and integration theory on infinite-dimensional spaces. New York: Academic.