Quantum systems with diagonal singularity

Advances in Chemical Physics

Volumn 99, Issue , 1997, Pages 299-332

  Antoniou, I ^a,b   Suchanecki, Z ^a,c  

^a INTERNATIONAL SOLVAY INSTITUTES   (Belgium)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^c WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001640124     PISSN: 00652385     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (69)

1. R. Brout and I. Prigogine, Physica 22, 621 (1956).
2. I. Prigogine and R. Balescu, Physica 25, 281 (1959).
3. J. Philippot, Physica 27, 490 (1961).
4. I. Prigogine, Non-equilibrium Statistical Mechanics (Wiley, New York, 1962).
5. L. van Hove, Physica 21, 901 (1955).
6. L. van Hove, Physica 22, 343 (1956).
7. L. van Hove, Physica 23, 441 (1957).
8. L. van Hove, Physica 25, 268 (1959).
9. I. Prigogine, C. George, F. Henin, and L. Rosenfeld, Chem. Scr. 4, 5 (1973).
10. C. George, Physica 65, 277 (1973).
11. A. Grecos, T. Guo, and W. Guo, Physica A80, 421 (1975).
12. R. Balescu, Equilibrium and Non-equilibrium Statistical Mechanics (Wiley, New York, 1975).
13. T. Petrosky, I. Prigogine, and S. Tasaki, Physica A173, 175 (1991).
14. T. Petrosky and I. Prigogine, Physica A175, 146 (1991).
15. I. Antoniou and I. Prigogine, Physica A192, 443 (1993).
16. I. Antoniou and S. Tasaki, Int. J. Quantum Chem., 46, 425 (1993).
17. N. Hugenholtz "Leon van Hove and the Dutch Physics," in Festschrift Leon van Hove (World Scientific, Singapore, 1989).
18. M. Naimark, Normed Algebra (Wolfer-Noordhoff, Groningen, 1972).
19. J. Dixmier, C*-algebras (North-Holland, Amsterdam, 1977).
20. I. Segal, Annals. Math. 48, 930 (1947).
21. G. Emch, Adv. Chem. Phys. 22, 315 (1972).
22. O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vols. I and II (Springer, New York, 1979, 1981).
23. R. Haag, Local Quantum Physics (Springer, Berlin, 1992).
24. P. A. M. Dirac, The Principles of Quantum Mechanics (Charendon Press, Oxford, 1958).
25. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955).
26. E. Prugovecki, Quantum Mechanics in Hilbert Space (Academic, New York, 1981).
27. A. Bohm, Quantum Mechanics: Foundations and Applications (Springer, Berlin, 1986).
28. I. Prigogine, From Being to Becoming (Freeman, San Francisco, 1980).
29. I. Prigogine, Phys. Rep. 219, 93 (1992).
30. T. Petrosky and I. Prigogine, Phys. Lett. A182, 1 (1993).
31. T. Petrosky and I. Prigogine, "The Liouville Space Extension of Quantum Mechanics," in Advances in Chemical Physics, Vol. 99 (Wiley, New York, 1997), pp. 1-120.
32. K. Maurin, Methods of Hilbert Spaces (Polish Scientific Publishers, Warsaw, 1972).
33. K. Maurin, General Eigenfunction Expansions and Unitary representations of Topological Groups (Polish Scientific Publishers, Warsaw, 1968).
34. B. de Dormale and H.-F. Gautrin, J. Math. Phys. 16, 2328 (1975).
35. J. M. Jauch and B. Misra, Helv. Phys. Acta 38, 30 (1965).
36. J. M. Jauch, Helv. Phys. Acta 33, 711 (1960).
37. J.-P. Antoine, G. Epifanio, and C. Trapani, Helv. Phys. Acta 56, 1175 (1983).
38. R. Schatten, Norm Ideals of Completely Continuous Operators (Springer Verlag, Berlin, 1960).
39. T. Kato, Perturbation Theory for Linear Operators, second corrected printing of the second edition (Springer Verlag, Berlin, 1984).
40. N. Dunford and J. Schwartz, Linear Operators I: General Theory (Wiley, New York, 1988).
41. J.-P. Antoine and Karwowski, Publ. R.I.M.S. Kyoto Univ. 21, 205 (1985).
42. G. Epifanio and C. Trapani, J. Math. Phys. 29, 536 (1988);
43. G. Epifanio and C. Trapani, J. Math. Phys. ibid. 32, 1096 (1991).
44. 2 Spaces (Springer Verlag, Berlin, 1978).
45. S. Mikhlin and S. Prössdorf, Singular Integral Operators (Springer Verlag, Berlin, 1986).
46. J. Dixmier, Von Neumann Algebras (North-Holland, Amsterdam, 1981).
47. M. Pour-el and J. Richards, Computability in Analysis and Physics (Springer Verlag, Berlin, 1989).
48. I. Antoniou, pp. 109-110 of reference 29.
49. N. Hugenholtz, Physica 23, 481 (1957).
50. G. Källen in Proceedings of the XII Solvay Conference in Physics (Interscience, New York, 1951).
51. T. Petrosky and I. Prigogine, Physica A147, 439 (1988).
52. W. Amrein, J. Jauch, and K. Sinha, Scattering Theory in Quantum Mechanics (Benjamin, Massachusetts, 1977).
53. A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1957).
54. I. Antoniou, M. Gadella, and Z. Suchanecki, "The Liouville Operator in Quantum Physics," in preparation.
55. W. Pauli, Festschrift zum 60 Geburstage A. Sommerfields (Hirzel, Leipzig, 1928), p. 30.
56. R. Phillips, Trans. Am. Math. Soc. 86, 109 (1957);
57. Comm. Pure Appl. Math. 12, 249 (1959).
58. G. Lindbland, Commun. Math. Phys. 48, 119 (1976).
59. C. Piron, Foundations of Quantum Physics (Benjamin, New York, 1976).
60. I. Antoniou and Z. Suchanecki, Found. Phys. 24, 1439 1994).
61. G. W. Mackey, The Mathematical Foundations of Quantum Mechanics (Benjamin, New York, 1963).
62. V. S. Varadarajan, Geometry of Quantum Theory (Springer Verlag, Berlin, 1985).
63. T. Petrosky and I. Prigogine, Proc. Natl. Acad. Sci. USA 90, 9393 (1993).
64. T. Petrosky and I. Prigogine, Chaos Solitons and Fractals (submitted).
65. I. Antoniou and Z. Suchanecki, Classical Systems with Diagonal Singularity (to be submitted).
66. I Antoniou and S. Tasaki, J. Phys. A26, 73 (1993).
67. I. Antoniou and S. Tasaki, Physica A190, 303 (1992).
68. S. Tasaki, Z. Suchanecki, and I. Antoniou, Phys. Lett. A 179, 103 (1993).
69. S. Tasaki, I. Antoniou, and Z. Suchanecki, Chaos Solitons and Fractals, 4, 227 (1994).