Euclidean quantum mechanics : analytical approach

 Access to full text

 Full (PDF)

1. [1] R.P. Feynman, Rev. Mod. Phys., Vol. 20, 1948, p. 267; with A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, N.Y., 1965. Zbl0176.54902
2. Annales de l'Institut Henri Poincaré - Physique théorique 
3. [2] M. Kac, On Some Connections Between Probability Theory and Differential and Integral Equations in Proc. of 2st Berkeley Symp. on Probability and Statistics, J. NEYMAN Ed., Univ. of California Press, Berkeley, 1951. Zbl0045.07002MR45333
4. [3] E. Schrödinger, Ann. Inst. Henri Poincaré, Vol. 2, 1932, p. 269. Zbl0004.42505JFM58.0933.03
5. [4] J.C. Zambrini, Phys. Rev. A, Vol. 35, No. 9, 1987, p. 3631. MR888537
6. [5] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I and II, Academic Press; N.Y., 1972 and 1975. MR493419
7. [6] S. Albeverio and R. Høegh-Krohn, in Stochastic Analysis and its Application, M. E. PINSKY Ed., M. DEKKER, N.Y1, 1984. Zbl0575.60079
8. [7] E. Nelson, Ann. Math., Vol. 70, 1959, p. 572. Zbl0091.10704MR107176
9. [8] T. Kato, Isr. J. Math., Vol. 13, 1973, p. 135. Zbl0246.35025
10. [9] B. Simon, Bull. of American Math. Soc., Vol. 7, No. 3, 1982, p. 447. Zbl0524.35002MR670130
11. [10] B. Jamison, Z. Wahrscheinlich, Gebiete, Vol. 30, 1974, p. 65. Zbl0326.60033MR359016
12. [11] S. Bernstein, Sur les liaisons entre les grandeurs aléatoires, Verh. des intern. Mathematikerkongr, Zurich, Band 1, 1932. Zbl0007.02104JFM58.1157.04
13. [12] J.C. Zambrini, J. Math. Phys., Vol. 27, No. 9, 1986, p. 2307. Zbl0623.60102
14. [13] A. Beurling, Annals of Math., Vol. 72, No. 1, 1960, p. 189. Zbl0091.13001MR125424
15. [14] K. Yasue, J. Funct. Anal., Vol. 41, 1981, p. 327. Zbl0482.60063MR619956
16. [15] S. Albeverio and R. Høegh-Krohn, J. Math. Phys., Vol. 15, 1974, p. 1745. Zbl0291.60028
17. [16] J. Von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, 1955. Zbl0064.21503MR66944
18. [17] R. Fortet, J. Math. Pures et Appl., Vol. IX, 1940, p. 83. Zbl0024.31803MR2692
19. [18] E. Nelson, J. Math. Phys., Vol. 5, 1964, p. 332. Zbl0133.22905
20. [19] S. Albeverio and R. Høegh-Krohn, Mathematical theory of Feynman Path Integrals, Lecture Notes in Math., No. 523, Springer Berlin, 1976. Zbl0337.28009
21. [20] (a) P. Exner. Open Quantum Systems and Feynman Integrals, D. Reidel, 1985; (b) D. Elworthy and A. Truman, Ann. Inst. Henri Poincaré, Vol. 41, No. 2, 1984, p. 115. Zbl0638.46051MR766559
22. [21] J. Schwinger, Proc. Nat. Acad. Sci. U.S.A., Vol. 44, 1958, p. 956. Zbl0082.42502MR97250
23. [22] E. Nelson, Probability Theory and Euclidean Field Theory in Constructive Quantum Field Theory, G. VELO and A. WIGHTMAN Eds., Lecture Notes in Phys., No. 25, 94, Springer Verlag, 1973. Zbl0367.60108MR395513
24. [23] B. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press. Princeton, 1974. MR489552
25. [24] K. Osterwalder and R. Schrader, Comm. Math. Phys., Vol. 37, 1973, p. 83; Vol. 42, 1975, p. 281. Zbl0303.46034MR376002
26. [25] S. Albeverio and R. Høegh-Krohn, J. Funct. Anal., Vol. 16, 1974, p. 39. Zbl0279.60095
27. [26] J. Glimm and A. Jaffe, Quantum Physics, a Functional Integral Point of View, Springer, 1981. Zbl0461.46051MR628000
28. [27] S. Albeverio, R. Høegh-Krohn and K. Iwata, Covariant Markovian Random Fields in Four Space-Time Dimensions with Nonlinear Electromagnetic Interaction, p. 69-83 in Proc. Dubna Conf., 1987, P. EXNER, P. SEBA Ed., Lect. Notes in Physics, No. 324, Springer, 1989. Zbl0722.60044MR1009842
29. [28] E. Nelson, Dynamical Theories of Brownian Motion, Princeton, 1967; Quantum fluctuations, Princeton Univ. Press, 1985. Zbl0165.58502MR214150
30. [29] E. Carlen, Comm. in Math. Physics, Vol. 94, 1984, p. 293. Zbl0558.60059MR763381
31. [30] P. Blanchard, P. Combe and W. Zheng, Mathematical and Physical aspects of Stochastic Mechanics, Lecture Notes Phys., No. 281, Springer Verlag, Berlin, 1987. Zbl0628.60104MR903845
32. [31] L. Accardi, in Quantum Probabilities and Applications to the Quantum Theory of Irreversible Processes, L. ACCARDI, A. FRIGERIO, V. GORINI Eds., Lecture Notes in Math., No. 1055, Springer, 1984, p. 134. MR782889
33. [32] T.A.. Osborn and Y. Fugiwara, Journal of Math. Phys., Vol. 24, 1983, p. 1093. Zbl0526.47029
34. [33] J.C. Zambrini, New Probabilistic Approach to the Classical Heat Equation in Proc. of Swansea Meeting, A. TRUMAN and I. M. DAVIES Eds., Lecture Notes in Math., No. 1325, Springer-Verlag, Berlin, 1988. Zbl0653.60052MR960171
35. [34] S. Albeverio, R. Høegh-Krohn, L. Streit, J. Math. Phys., Vol. 18, 1977, p. 907. Zbl0368.60091
36. [35] J.C. Zambrini, in preparation. 
37. [36] F. Guerra, in Proc. quoted under Ref. [31]; G. Jona-Lasinio, Astérisque, 132, 1985, p. 203. 

1. Nicolas Privault, Jean-Claude Zambrini, Markovian bridges and reversible diffusion processes with jumps