The main theme of this book is the “path integral
technique” and its applications to constructive methods of
quantum physics. The central topic is probabilistic foundations of the
Feynman–Kac formula. Starting with the main examples of Gaussian
processes (the Brownian motion, the oscillatory process, and the Brownian
bridge), the author presents four different proofs of the
Feynman–Kac formula. Also included is a simple exposition of
stochastic Itô calculus and its applications, in particular to
the Hamiltonian of a particle in a magnetic field (the
Feynman–Kac–Itô formula).
Among other topics discussed are the probabilistic approach to the bound
of the number of ground states of correlation inequalities (the
Birman–Schwinger principle, Lieb's formula, etc.), the calculation of
asymptotics for functional integrals of Laplace type (the theory of
Donsker–Varadhan) and applications, scattering theory, the theory of
crushed ice, and the Wiener sausage.
Written with great care and containing many highly illuminating examples,
this classic book is highly recommended to anyone interested in
applications of functional integration to quantum physics. It can also
serve as a textbook for a course in functional integration.
Readership
Graduate students and research mathematicians
interested in probability and applications of functional integration
to quantum physics.