Feynman maps, Cameron-Martin formulae and anharmonic oscillators
Elworthy, David ; Truman, Aubrey
Annales de l'I.H.P. Physique théorique, Tome 41 (1984), p. 115-142 / Harvested from Numdam
@article{AIHPA_1984__41_2_115_0,
     author = {Elworthy, Kenneth David and Truman, Aubrey},
     title = {Feynman maps, Cameron-Martin formulae and anharmonic oscillators},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {41},
     year = {1984},
     pages = {115-142},
     mrnumber = {769152},
     zbl = {0578.28013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1984__41_2_115_0}
}
Elworthy, David; Truman, Aubrey. Feynman maps, Cameron-Martin formulae and anharmonic oscillators. Annales de l'I.H.P. Physique théorique, Tome 41 (1984) pp. 115-142. http://gdmltest.u-ga.fr/item/AIHPA_1984__41_2_115_0/

[1] S. Albeverio and R. Hoegh-Krohn, Mathematical Theory of Feynman Path Integrals, Springer Lecture Notes in Mathematics, p. 523, Berlin-Heidelberg-New York, 1976. | MR 495901 | Zbl 0337.28009

[2] R.J. Blattner, Pacific J. Math., t. 8, 1958, p. 665-677. | MR 103421 | Zbl 0087.32001

[3] R.H. Cameron and W.T. Martin, Trans. Amer. Math. Soc., t. 58, n° 2, 1945, p. 184-219. | MR 13240 | Zbl 0060.29104

[4] N. Dunford and J.T. Schwarz, Linear Operators Part I, Interscience, New York, 1967.

[5] a) K.D. Elworthy and A. Truman, A Cameron-Martin Formula for Feynman integrals, p. 288-294 in Mathematical Problems in Theoretical Physics (Proceedings, Berlin (West) 1981) edited by R. Schrader, R. Seiler and D. A. Uhlenrock (Springer Lecture Notes in Physics 153).

b) K.D. Elworthy and A. Truman, J. Math. Phys., t. 22, 1981, p. 2144-2166. | MR 641455 | Zbl 0485.70024

[6] L.D. Faddeev and A.R. Slavnov, Gauge Fields, Introduction to Quantum Theory (Benjamin/Cummings, Reading Mass., 1980). | MR 618649 | Zbl 0486.53052

[7] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965). | Zbl 0176.54902

[8] a) D. Fujiwara, Proc. Japan Acad., t. 55 A, 1979, p. 195-199. | Zbl 0432.35007

b) D. Fujiwara, Proc. Japan Acad., t. 55 A, 1979, p. 273-277, and references cited therein. | MR 553398 | Zbl 0454.35084

[9] L. Hörmander, Acta Math., t. 127, 1971, p. 79-183. | MR 388463 | Zbl 0212.46601

[10] V.P. Maslov, Theorie des Perturbations et Methods Asymptotiques (Dunod, Paris, 1972) and references cited therein. | Zbl 0247.47010

[11] A. Maheshwari, C. Dewitt-Morette and B. Nelson, Phys. Rep., t. 50, 1979, p. 257- 372.

[12] a) M. Reed and B. Simon, Methods of Modern Mathematical Physics, I Functional Analysis (Academic Press, New York and London, 1973). M. Reed and B. Simon, Methods of Modern Mathematical Physics, II Fourier Analysis and Self-adjointness (Academic Press, New York and London, 1975. | MR 751959 | Zbl 0242.46001

[13] J. Rezende, Remark on the solution of the Schrödinger equation for anharmonic oscillators via Feynman path integral, BI TP 82/22, Bielefeld preprint, August 1982. | MR 691976

[14] L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Tata Institute Studies in Maths, t. 6, Bombay Oxford University Press, 1973. | MR 426084 | Zbl 0298.28001

[15] B. Simon, Functional Integration and Quantum Physics (Academic Press, New York, 1979). | MR 544188 | Zbl 0434.28013

[16] B. Simon, Trace ideals and their applications (Cambridge University Press, London Math. Soc. Lecture Note Series, 1979). | MR 541149 | Zbl 0423.47001

[17] D.L. Skoug and G.W. Johnson, J. Func. Anal., t. 12, 1973, p. 129-152. | Zbl 0255.46041

[18] J. Tarski and H.P. Berg, J. Phys. A, t. 14, 1981, p. 2207-2222. | MR 628365 | Zbl 0469.46030

[19] A. Truman, The polygonal path formulation of the Feynman path integral in Feynman path integrals edited by S. Albeverio et al. (Springer Lecture Notes in Physics, t. 106, 1979). | MR 553077 | Zbl 0412.28009