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Mathematical theory of Feynman path integrals

✍ Scribed by Sergio A. Albeverio, Raphael J. H. Egh-Krohn

Publisher
Not Avail
Year
1976
Tongue
English
Leaves
143
Series
Lecture Notes in Mathematics 0523
Category
Library
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✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Mathematical Theory of Feynman Path Inte
πŸ“ Mathematical Theory of Feynman Path Integrals
✍ Sergio A. Albeverio, Raphael J. HΓΈegh-Krohn (auth.) πŸ“‚ Library πŸ“… 1976 πŸ› Springer Berlin Heidelberg 🌐 English

<P>Feynman path integrals integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have al

Mathematical Theory of Feynman Path Inte
πŸ“ Mathematical Theory of Feynman Path Integrals: An Introduction
✍ Sergio A. Albeverio, Raphael J. HΓΈegh-Krohn, Sonia Mazzucchi (auth.) πŸ“‚ Library πŸ“… 2008 πŸ› Springer-Verlag Berlin Heidelberg 🌐 English

<p><P>Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also play

Mathematical Theory of Feynman Path Inte
πŸ“ Mathematical Theory of Feynman Path Integrals: An Introduction
✍ Sergio A. Albeverio, Raphael J. HΓΈegh-Krohn, Sonia Mazzucchi (auth.) πŸ“‚ Library πŸ“… 2008 πŸ› Springer-Verlag Berlin Heidelberg 🌐 English

<p><P>Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also play

Mathematical theory of Feynman path inte
πŸ“ Mathematical theory of Feynman path integrals: An introduction
✍ Sergio Albeverio, Rafael HΓΈegh-Krohn, Sonia Mazzucchi πŸ“‚ Library πŸ“… 2008 πŸ› Springer 🌐 English

<P>The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material