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Ground states of quantum field model...

Hiroshima, Fumio.

Ground states of quantum field modelsperturbation of embedded eigenvalues /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Ground states of quantum field modelsby Fumio Hiroshima.
Reminder of title:	perturbation of embedded eigenvalues /
Author:	Hiroshima, Fumio.
Published:	Singapore :Springer Singapore :2019.
Description:	xvi, 136 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Quantum field theory.
Online resource:	https://doi.org/10.1007/978-981-32-9305-2
ISBN:	9789813293052$q(electronic bk.)

Ground states of quantum field modelsperturbation of embedded eigenvalues /
Hiroshima, Fumio.

Ground states of quantum field modelsperturbation of embedded eigenvalues /[electronic resource] :by Fumio Hiroshima. - Singapore :Springer Singapore :2019. - xvi, 136 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.352197-1757 ;. - SpringerBriefs in mathematical physics ;v.1..

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

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.

ISBN: 9789813293052$q(electronic bk.)

Standard No.: 10.1007/978-981-32-9305-2doiSubjects--Topical Terms:

203819
Quantum field theory.

LC Class. No.: QC174.45 / .H57 2019

Dewey Class. No.: 530.143

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520 $a 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.
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