Lectures on Quantum Field Theory and Functional Integration

2023
ISBN: 978-3-031-30714-0
Verlag: Springer Nature Switzerland

Buch, Englisch, 235 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 388 g

This book offers a concise introduction to quantum field theory and functional integration for students of physics and mathematics. Its aim is to explain mathematical methods developed in the 1970s and 1980s and apply these methods to standard models of quantum field theory. In contrast to other textbooks on quantum field theory, this book treats functional integration as a rigorous mathematical tool. More emphasis is placed on the mathematical framework as opposed to applications to particle physics. It is stressed that the functional integral approach, unlike the operator framework, is suitable for numerical simulations. The book arose from the author's teaching in Wroclaw and preserves the form of his lectures. So some topics are treated as an introduction to the problem rather than a complete solution with all details. Some of the mathematical methods described in the book resulted from the author's own research.

Zielgruppe

Graduate

Autoren/Hrsg.

Haba, Zbigniew

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Notation and mathematical preliminaries.- Quantum theory of the scalar free field.- Interacting fields and scattering amplitudes.- Thermal states and quantum scalar field on a curved manifold.- The functional integral.- Feynman integral in terms of the Wiener integral.- Application of the Feynman integral for approximate calculations.- Feynman path integral in terms of expanding paths.- An interaction with a quantum electromagnetic field.- Particle interaction with gravitons.- Quantization of non-Abelian gauge fields.- Lattice approximation.

Über Autor(innen)

Born in 1951, Zbigniew Haba obtained his Ph.D. degree at the University of Wroclaw in 1976, where he then became an assistant professor. Since 1995, he holds a full professorship.
He has spent long periods visiting the Department of Physics of Bielefeld University, and also had research stays in the Department of Mathematics, Bochum University,1988, and the Max Planck Institute, Munich. In 1993, he was the Gulbenkian fellow at Lisbon University, and the visiting professor in Freie Universitaet Berlin in 2000.
He is the author of a monograph "Feynman integral and random dynamics in quantum physics. A probabilistic approach to quantum dynamics", Kluwer/Springer, 1999.