Evolution Processes and the Feynman-Kac Formula

ISBN-13: 9789048146505 / Angielski / Miękka / 2010 / 238 str.

Brian Jefferies

Opis

The evolution of a physical system can often be described in terms of a semigroup of linear operators. Observations of the system may be modelled by a spectral measure. A combination of these basic objects produces a family of operator valued set functions, by which perturbations of the evolution are represented as path integrals. In this book, random processes measured by operator valued set functions - evolution processes - are systematically examined for the first time. The Feynman-Kac formula, representing perturbations of the heat semigroup in terms of integrals with respect to Wiener measure, is extended in a number of directions: to other countably additive processes, not necessarily associated with a probability measure; to unbounded processes such as those associated with Feynman integrals; and to random evolutions. Audience: Researchers in mathematical physics, functional analysis and stochastic processes.

Spis treści

Preface. Introduction. 1. Vector Measures and Function Spaces. 2. Evolution Processes. 3. Feynman-Kac Formulae. 4. Bilinear Integration. 5. Random Evolutions. 6. Some Bounded Evolution Processes. 7. Integration with Respect to Unbounded Set Functions. 8. The Schrödinger Process. 9. The Radial Dirac Process. Bibliography. Index.