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

Applications in Rigorous Quantum Field Theory
3rd, updated Auflage
ISBN: 978-3-11-223148-7
Verlag: De Gruyter

Buch, Englisch, Band 34, 588 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 1121 g

Reihe: De Gruyter Studies in Mathematics

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.

Autoren/Hrsg.

Hiroshima, Fumio

Lorinczi, József

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik

Über Autor(innen)

Professor Dr. József Lorinczi, Alfréd Rényi Institute of Mathematics, Budapest, Hungary; Professor Dr. Fumio Hiroshima, Faculty of Mathematics, Kyushu University, Fukuoka, Japan; Professor Dr. Volker Betz, Technical University Darmstadt, Mathematics, Darmstadt, Germany.