Euclidean quantum mechanics : analytical approach
Albeverio, S. ; Yasue, K. ; Zambrini, J. C.
Annales de l'I.H.P. Physique théorique, Tome 51 (1989), p. 259-308 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPA_1989__50_3_259_0,
     author = {Albeverio, Sergio and Yasue, K. and Zambrini, Jean-Claude},
     title = {Euclidean quantum mechanics : analytical approach},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {51},
     year = {1989},
     pages = {259-308},
     mrnumber = {1017966},
     zbl = {0687.60091},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1989__50_3_259_0}
}

Albeverio, S.; Yasue, K.; Zambrini, J. C. Euclidean quantum mechanics : analytical approach. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 259-308. http://gdmltest.u-ga.fr/item/AIHPA_1989__50_3_259_0/

[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. | Zbl 0176.54902

Annales de l'Institut Henri Poincaré - Physique théorique

[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. | MR 45333 | Zbl 0045.07002

[3] E. Schrödinger, Ann. Inst. Henri Poincaré, Vol. 2, 1932, p. 269. | JFM 58.0933.03 | Numdam | Zbl 0004.42505

[4] J.C. Zambrini, Phys. Rev. A, Vol. 35, No. 9, 1987, p. 3631. | MR 888537

[5] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I and II, Academic Press; N.Y., 1972 and 1975. | MR 493419

[6] S. Albeverio and R. Høegh-Krohn, in Stochastic Analysis and its Application, M. E. PINSKY Ed., M. DEKKER, N.Y1, 1984.

[7] E. Nelson, Ann. Math., Vol. 70, 1959, p. 572. | MR 107176 | Zbl 0091.10704

[8] T. Kato, Isr. J. Math., Vol. 13, 1973, p. 135. | Zbl 0246.35025

[9] B. Simon, Bull. of American Math. Soc., Vol. 7, No. 3, 1982, p. 447. | MR 670130 | Zbl 0524.35002

[10] B. Jamison, Z. Wahrscheinlich, Gebiete, Vol. 30, 1974, p. 65. | MR 359016 | Zbl 0326.60033

[11] S. Bernstein, Sur les liaisons entre les grandeurs aléatoires, Verh. des intern. Mathematikerkongr, Zurich, Band 1, 1932. | JFM 58.1157.04 | Zbl 0007.02104

[12] J.C. Zambrini, J. Math. Phys., Vol. 27, No. 9, 1986, p. 2307. | Zbl 0623.60102

[13] A. Beurling, Annals of Math., Vol. 72, No. 1, 1960, p. 189. | MR 125424 | Zbl 0091.13001

[14] K. Yasue, J. Funct. Anal., Vol. 41, 1981, p. 327. | MR 619956 | Zbl 0482.60063

[15] S. Albeverio and R. Høegh-Krohn, J. Math. Phys., Vol. 15, 1974, p. 1745. | Zbl 0291.60028

[16] J. Von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, 1955. | MR 66944 | Zbl 0064.21503

[17] R. Fortet, J. Math. Pures et Appl., Vol. IX, 1940, p. 83. | MR 2692 | Zbl 0024.31803

[18] E. Nelson, J. Math. Phys., Vol. 5, 1964, p. 332. | Zbl 0133.22905

[19] S. Albeverio and R. Høegh-Krohn, Mathematical theory of Feynman Path Integrals, Lecture Notes in Math., No. 523, Springer Berlin, 1976. | Zbl 0337.28009

[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. | MR 766559 | Zbl 0638.46051

[21] J. Schwinger, Proc. Nat. Acad. Sci. U.S.A., Vol. 44, 1958, p. 956. | MR 97250 | Zbl 0082.42502

[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. | MR 395513 | Zbl 0367.60108

[23] B. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ. Press. Princeton, 1974. | MR 489552

[24] K. Osterwalder and R. Schrader, Comm. Math. Phys., Vol. 37, 1973, p. 83; Vol. 42, 1975, p. 281. | MR 376002 | Zbl 0303.46034

[25] S. Albeverio and R. Høegh-Krohn, J. Funct. Anal., Vol. 16, 1974, p. 39. | Zbl 0279.60095

[26] J. Glimm and A. Jaffe, Quantum Physics, a Functional Integral Point of View, Springer, 1981. | MR 628000 | Zbl 0461.46051

[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. | MR 1009842 | Zbl 0722.60044

[28] E. Nelson, Dynamical Theories of Brownian Motion, Princeton, 1967; Quantum fluctuations, Princeton Univ. Press, 1985. | MR 214150 | Zbl 0165.58502

[29] E. Carlen, Comm. in Math. Physics, Vol. 94, 1984, p. 293. | MR 763381 | Zbl 0558.60059

[30] P. Blanchard, P. Combe and W. Zheng, Mathematical and Physical aspects of Stochastic Mechanics, Lecture Notes Phys., No. 281, Springer Verlag, Berlin, 1987. | MR 903845 | Zbl 0628.60104

[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. | MR 782889

[32] T.A.. Osborn and Y. Fugiwara, Journal of Math. Phys., Vol. 24, 1983, p. 1093. | Zbl 0526.47029

[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. | MR 960171 | Zbl 0653.60052

[34] S. Albeverio, R. Høegh-Krohn, L. Streit, J. Math. Phys., Vol. 18, 1977, p. 907. | Zbl 0368.60091

[35] J.C. Zambrini, in preparation.

[36] F. Guerra, in Proc. quoted under Ref. [31]; G. Jona-Lasinio, Astérisque, 132, 1985, p. 203.