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作者 Hiroshima, Fumio, author
書名 Ground states of quantum field models : perturbation of embedded eigenvalues / by Fumio Hiroshima
出版項 Singapore : Springer Singapore : Imprint: Springer, 2019
國際標準書號 9789813293052 (electronic bk.)
9789813293045 (paper)
國際標準號碼 10.1007/978-981-32-9305-2 doi
book jacket
說明 1 online resource (xvi, 136 pages) : illustrations, digital ; 24 cm
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
系列 SpringerBriefs in mathematical physics, 2197-1757 ; volume 35
SpringerBriefs in mathematical physics ; volume 35
附註 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
Host Item Springer Nature eBook
主題 Quantum field theory
Mathematical Physics
Quantum Field Theories, String Theory
Functional Analysis
Alt Author SpringerLink (Online service)
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