Abstract
In the framework of the rigorous definition of an integral in the abstract complete separable metric space the new method for numerical evaluation of functional integrals is elaborated. The method does not require preliminary discretization and allows to use the deterministic algorithms in computations. The convergence of approximations to an exact value of integral is proved, the estimate of the remainder is obtained. In the particular case of conditional Wiener integrals the approximation formulas with the weight functional are derived. The method is generalized to the case of computation of multiple functional integrals. Some applications of the method to the problems of quantum mechanics and quantum field theory are considered.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lobanov, Y.Y. (1997). A New Method of Computation of Functional Integrals. In: DeWitt-Morette, C., Cartier, P., Folacci, A. (eds) Functional Integration. NATO ASI Series, vol 361. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0319-8_22
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0319-8_22
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0321-1
Online ISBN: 978-1-4899-0319-8
eBook Packages: Springer Book Archive