Description
Book SynopsisThe 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 and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
Trade ReviewFrom the reviews of the second edition:
"The second edition (from 2008) contains a large additional chapter … entitled ‘Some Recent Developments’, where alternative attempts at a rigourous formalism are presented, as well as recent applications. Summarizing, this is a good and insightful book for those familiar with path integrals and curious about the mathematic foundations of path integration." (Jacques Tempere, Belgian Physical Society Magazine, Issue 2, June, 2009)
“The new edition goes way beyond the habitual corrections and additions … . It is good to have this new book. Not only for the more recent results it contains, but also as a point of departure for so many questions that are still open in the realm of infinite dimensional oscillatory integrals.” (Ludwig Streit, Zentralblatt MATH, Vol. 1222, 2011)
Table of ContentsThe Fresnel Integral of Functions on a Separable Real Hilbert Space.- The Feynman Path Integral in Potential Scattering.- The Fresnel Integral Relative to a Non-singular Quadratic Form.- Feynman Path Integrals for the Anharmonic Oscillator.- Expectations with Respect to the Ground State of the Harmonic Oscillator.- Expectations with Respect to the Gibbs State of the Harmonic Oscillator.- The Invariant Quasi-free States.- The Feynman History Integral for the Relativistic Quantum Boson Field.- Some Recent Developments.
