Ground States of Quantum Field Models

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Beschreibung

This book provides self-contained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spin-boson model, the Nelson model with and without an ultraviolet cutoff, and the Pauli¿Fierz model with and without dipole approximation in non-relativistic quantum electrodynamics. These models describe interactions between bose fields and quantum mechanical matters.

A ground state is defined as the eigenvector associated with the bottom of the spectrum of a self-adjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is non-trivial to show the existence of ground states in non-perturbative ways. We show the existence of the ground state of the Pauli¿Fierz mode, the Nelson model, and the spin-boson model, and several kinds of proofs of the existence of ground states are explicitly provided. Key ingredients are compact sets and compact operators in Hilbert spaces. For the Nelson model with an ultraviolet cutoff and the Pauli¿Fierz model with dipole approximation we show not only the existence of ground states but also enhanced binding. The enhanced binding means that a system for zero-coupling has no ground state but it has a ground state after turning on an interaction.

The book will be of interest to graduate students of mathematics as well as to students of the natural sciences who want to learn quantum field theory from a mathematical point of view. It begins with abstract compactness arguments in Hilbert spaces and definitions of fundamental facts of quantum field theory: boson Fock spaces, creation operators, annihilation operators, and second quantization. This book quickly takes the reader to a level where a wider-than-usual range of quantum field theory can be appreciated, and self-contained proofs of the existence of ground states and enhanced binding are presented.

Über den Autor

The author was an invited speaker at the ICMP 2015.

Zusammenfassung

Is a comprehensive survey of recent results of the existence of ground states of models in quantum field theory

Focuses on non-perturbative methods, independent of coupling constants and other factors

Begins with fundamentals of quantum field theory and takes the reader to a higher level of appreciation of that theory

Inhaltsverzeichnis

Introduction.- Preliminaries.- The Pauli-Fierz model.- The Nelson model.- Spin-boson model.- Enhanced bindings.

Details

Erscheinungsjahr:	2019
Fachbereich:	Theoretische Physik
Genre:	Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	152
Reihe:	SpringerBriefs in Mathematical Physics
Inhalt:	xvi 136 S. 14 s/w Illustr. 136 p. 14 illus.
ISBN-13:	9789813293045
ISBN-10:	9813293047
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Hiroshima, Fumio
Auflage:	1st ed. 2019
Hersteller:	Springer Singapore Springer Nature Singapore SpringerBriefs in Mathematical Physics
Maße:	235 x 155 x 9 mm
Von/Mit:	Fumio Hiroshima
Erscheinungsdatum:	28.08.2019
Gewicht:	0,242 kg

Artikel-ID: 116849342