Mathematical Theory of Feynman Path Integrals

Preface to the second edition.- Preface to the first edition.- 1.Introduction.- 2.The Fresnel Integral of Functions on a Separable Real Hilbert Spa.- 3.The Feynman Path Integral in Potential Scattering.- 4.The Fresnel Integral Relative to a Non-singular Quadratic Form.- 5.Feynman Path Integrals for the Anharmonic Oscillator.- 6.Expectations with Respect to the Ground State of the Harmonic Oscillator.- 7.Expectations with Respect to the Gibbs State of the Harmonic Oscillator.- 8.The Invariant Quasi-free States.- 9.The Feynman Hystory Integral for the Relativistic Quantum Boson Field.- 10.Some Recent Developments.- 10.1.The infinite dimensional oscillatory integral.- 10.2.Feynman path integrals for polynomially growing potentials.- 10.3.The semiclassical expansio.- 10.4.Alternative approaches to Feynman path integrals.- 10.4.1.Analytic continuation.- 10.4.2.White noise calculus.- 10.5.Recent applications.- 10.5.1.The Schroedinger equation with magnetic fields.- 10.5.2.The Schroedinger equation with time dependent potentials.- 10.5.3 .hase space Feynman path integrals.- 10.5.4.The stochastic Schroedinger equation.- 10.5.5.The Chern-Simons functional integral.- References of the first edition.- References of the second edition.- Analytic index.- List of Notations.

From 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)

From 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)