Feynman–Kac-Type Theorems and Gibbs Measures on Path Space

The two-volume work established itself as a standard reference serving both as a self-contained, advanced textbook, and as a research tool. Volume 2 covers fundamental models of the non-relativistic and relativistic quantum field theory of an electrically charged particle coupled to a boson field such as the Nelson model (scalar coupling), the Pauli-Fierz model (vector coupling), as well as related matters such as the Spin Boson model and the Rabi model. By constructing Gibbs measures on Schwartz distribution-valued sample paths, a systematic study of the existence, uniqueness and properties of ground states in these models will be presented. The rigorous framework described will serve as a point of departure for further research, developing cutting-edge mathematical tools such as analysis on infinite dimensional spaces or distribution-valued stochastic processes with continuous paths or jumps, offering a user-friendly presentation suitable for individual or group study. New section on Rabi model has been added.