Feynman maps, Cameron-Martin formulae and anharmonic oscillators

David Elworthy; Aubrey Truman

Annales de l'I.H.P. Physique théorique (1984)

  • Volume: 41, Issue: 2, page 115-142
  • ISSN: 0246-0211

How to cite

top

Elworthy, David, and Truman, Aubrey. "Feynman maps, Cameron-Martin formulae and anharmonic oscillators." Annales de l'I.H.P. Physique théorique 41.2 (1984): 115-142. <http://eudml.org/doc/76253>.

@article{Elworthy1984,
author = {Elworthy, David, Truman, Aubrey},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Cameron-Martin formula; Feynman integral; path integral; Fresnel integrals},
language = {eng},
number = {2},
pages = {115-142},
publisher = {Gauthier-Villars},
title = {Feynman maps, Cameron-Martin formulae and anharmonic oscillators},
url = {http://eudml.org/doc/76253},
volume = {41},
year = {1984},
}

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
PB - Gauthier-Villars
VL - 41
IS - 2
SP - 115
EP - 142
LA - eng
KW - Cameron-Martin formula; Feynman integral; path integral; Fresnel integrals
UR - http://eudml.org/doc/76253
ER -

References

top
  1. [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. Zbl0337.28009MR495901
  2. [2] R.J. Blattner, Pacific J. Math., t. 8, 1958, p. 665-677. Zbl0087.32001MR103421
  3. [3] R.H. Cameron and W.T. Martin, Trans. Amer. Math. Soc., t. 58, n° 2, 1945, p. 184-219. Zbl0060.29104MR13240
  4. [4] N. Dunford and J.T. Schwarz, Linear Operators Part I, Interscience, New York, 1967. 
  5. [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 Physics153). 
  6. b) K.D. Elworthy and A. Truman, J. Math. Phys., t. 22, 1981, p. 2144-2166. Zbl0485.70024MR641455
  7. [6] L.D. Faddeev and A.R. Slavnov, Gauge Fields, Introduction to Quantum Theory (Benjamin/Cummings, Reading Mass., 1980). Zbl0486.53052MR618649
  8. [7] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw–Hill, New York, 1965). Zbl0176.54902
  9. [8] a) D. Fujiwara, Proc. Japan Acad., t. 55 A, 1979, p. 195-199. Zbl0432.35007
  10. b) D. Fujiwara, Proc. Japan Acad., t. 55 A, 1979, p. 273-277, and references cited therein. Zbl0454.35084MR553398
  11. [9] L. Hörmander, Acta Math., t. 127, 1971, p. 79-183. Zbl0212.46601MR388463
  12. [10] V.P. Maslov, Theorie des Perturbations et Methods Asymptotiques (Dunod, Paris, 1972) and references cited therein. Zbl0247.47010
  13. [11] A. Maheshwari, C. Dewitt-Morette and B. Nelson, Phys. Rep., t. 50, 1979, p. 257- 372. 
  14. [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. Zbl0242.46001MR751959
  15. [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. MR691976
  16. [14] L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Tata Institute Studies in Maths, t. 6, BombayOxford University Press, 1973. Zbl0298.28001MR426084
  17. [15] B. Simon, Functional Integration and Quantum Physics (Academic Press, New York, 1979). Zbl0434.28013MR544188
  18. [16] B. Simon, Trace ideals and their applications (Cambridge University Press, London Math. Soc. Lecture Note Series, 1979). Zbl0423.47001MR541149
  19. [17] D.L. Skoug and G.W. Johnson, J. Func. Anal., t. 12, 1973, p. 129-152. Zbl0255.46041
  20. [18] J. Tarski and H.P. Berg, J. Phys. A, t. 14, 1981, p. 2207-2222. Zbl0469.46030MR628365
  21. [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). Zbl0412.28009MR553077

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.