說明 
1 online resource (xvi, 136 pages) : illustrations, digital ; 24 cm 

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系列 
SpringerBriefs in mathematical physics, 21971757 ; volume 35


SpringerBriefs in mathematical physics ; volume 35

附註 
Introduction  Preliminaries  The PauliFierz model  The Nelson model  Spinboson model  Enhanced bindings 

This book provides selfcontained proofs of the existence of ground states of several interaction models in quantum field theory. Interaction models discussed here include the spinboson model, the Nelson model with and without an ultraviolet cutoff, and the PauliFierz model with and without dipole approximation in nonrelativistic 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 selfadjoint operator describing the Hamiltonian of a model. The bottom of the spectrum is however embedded in the continuum and then it is nontrivial to show the existence of ground states in nonperturbative ways. We show the existence of the ground state of the PauliFierz mode, the Nelson model, and the spinboson 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 PauliFierz 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 zerocoupling 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 widerthanusual range of quantum field theory can be appreciated, and selfcontained proofs of the existence of ground states and enhanced binding are presented 
Host Item 
Springer Nature eBook

主題 
Quantum field theory


Eigenvalues


Mathematical Physics


Quantum Field Theories, String Theory


Functional Analysis

Alt Author 
SpringerLink (Online service)

