Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albeverio, S. and Høegh-Krohn, R. J., Mathematical theory of Feynman path integral, Lecture Notes in Math., Springer, Berlin, 523 (1976).
Albeverio, S. and Høegh-Krohn, R. J., Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with application to the classical limit of quantum mechanics, I. Inv. Math., 40 (1977), 59–106.
Albeverio, S., Høegh-Krohn, R. J. and others ed., Feynman Path integrals, Preceedings Marseille 1978, Lecture Notes in Physics, Springer, Berlin, 106 (1978).
Asada, K. and Fujiwara, D., On some oscillatory integral transformations on L 2(R n), Japan. J. Math., 27 (1978), 299–361.
Cameron, R. H., A family of integrals serving to connect the Wiener and Feynman integrals, J. Mathematics and Physics, 39 (1960), 126–140.
Feynman, R. P., Space time approach to non relativistic quantum mechanics, Rev. of Modern Phys., 20 (1948), 367–387.
Feynman R. P. and Hibbs A. R., Quantum mechanics and path integral, McGraw-Hill, New York, (1965).
Fujiwara, D., Fundamental solution of partial differential operator of Schrödinger's type, I. Proc. Japan Acad., 50 (1974), 566–569.
Fujiwara, D., A construction of the fundamental solution for the Schrödinger equations, J. d'Analyse Math., 35 (1979), 41–96.
Fujiwara, D., Remarks on convergence of some Feynman path integrals, Duke Math. J. 47 (1980), 559–600.
Fujiwara, D., Some Feynman path integrals as an improper integral over a Sobolev space, Proc. conference of symposium on PDE, Saint Jean de Mont (1989).
Fujiwara, D., The stationary phase method with an estimate of the remainder term on a space of large dimension, to appear in Nagoya Math. J., 24 (1991), 61–97.
Gelfand, I. M. and Yaglom, A. M., Integrals in functional spaces and its applications in quantum physics, J. Math. Physics, 1, 48-69.
Itô, K., Generalized uniform complex measure in Hilbertian metric spaces and its application to the Feynman path integrals, Proc. 5th Berkeley symposium on Math. Statistics and Probability, Univ. of California Press, Berkeley, 2 part 1, (1967), 145–161.
Nelson, E., Feynman path integrals and Schrödinger equation, J. Mathematical Physics, 5 (1964), 332–343.
Pauli, W., (edited by Enz, C. P.), Pauli Lectures on Physics, vol.6, Selected topics in field quantization, MIT Press (1973).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag
About this paper
Cite this paper
Fujiwara, D. (1993). Some feynman path integrals as oscillatory integrals over a sobolev manifold. In: Komatsu, H. (eds) Functional Analysis and Related Topics, 1991. Lecture Notes in Mathematics, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085473
Download citation
DOI: https://doi.org/10.1007/BFb0085473
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56471-3
Online ISBN: 978-3-540-47565-1
eBook Packages: Springer Book Archive