Feynman maps, Cameron-Martin formulae and anharmonic oscillators
Annales de l'I.H.P. Physique théorique, Tome 41 (1984) no. 2, pp. 115-142.
@article{AIHPA_1984__41_2_115_0,
     author = {Elworthy, David and Truman, Aubrey},
     title = {Feynman maps, {Cameron-Martin} formulae and anharmonic oscillators},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {115--142},
     publisher = {Gauthier-Villars},
     volume = {41},
     number = {2},
     year = {1984},
     mrnumber = {769152},
     zbl = {0578.28013},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1984__41_2_115_0/}
}
TY  - JOUR
AU  - Elworthy, David
AU  - Truman, Aubrey
TI  - Feynman maps, Cameron-Martin formulae and anharmonic oscillators
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1984
SP  - 115
EP  - 142
VL  - 41
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1984__41_2_115_0/
LA  - en
ID  - AIHPA_1984__41_2_115_0
ER  - 
%0 Journal Article
%A Elworthy, David
%A Truman, Aubrey
%T Feynman maps, Cameron-Martin formulae and anharmonic oscillators
%J Annales de l'I.H.P. Physique théorique
%D 1984
%P 115-142
%V 41
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1984__41_2_115_0/
%G en
%F 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) no. 2, pp. 115-142. http://www.numdam.org/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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

[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

[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 | Zbl

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

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

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

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

[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 | Zbl