ENGLISH

Mathematical theory of Feynman path integrals

By Sergio A. Albeverio , Raphael J. H. Egh-Krohn

Book information

Publisher
Not Avail
Year
1976
ISBN
3540077855, 9783540077855
Language
english
Format
DJVU
Filesize
1008 kB (1032418 bytes)
Series
Lecture Notes in Mathematics 0523
Pages
143\143
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

Description

In this work we develop a general theory of oscillatory integrals on real Hilbert spaces and apply it to the mathematical foundation of the so called Feynman path integrals of non relativistic quantum mechanics, quantum statistical mechanics and quantum field theory. The translation invariant integrals we define provide a natural extension of the theory of finite dimensional oscillatory integrals, which has newly undergone an impressive development, and appear to be a suitable tool in infinite imensional analysis. For one example, on the basis of the present work we have extended the methods of stationary phase, Lagrange immersions and orresponding asymptotic expansions to the infinite dimensional case, covering in particular the expansions around the classical limit of quantum mechanics. A particular case of the oscillatory integrals studied in the present work are the Feynman path integrals used extensively in the physical literature, starting with the basic work on quantum dynamics by Dirac and Feynman, in the forties.

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