MARC 主機 00000nam a2200481 i 4500 
001    978-981-32-9305-2 
003    DE-He213 
005    20200629195332.0 
006    m     o  d         
007    cr nn 008maaau 
008    190816s2019    si      s         0 eng d 
020    9789813293052|q(electronic bk.) 
020    9789813293045|q(paper) 
024 7  10.1007/978-981-32-9305-2|2doi 
040    GP|cGP|erda 
041 0  eng 
050  4 QC174.45|b.H57 2019 
082 04 530.143|223 
100 1  Hiroshima, Fumio,|eauthor 
245 10 Ground states of quantum field models :|bperturbation of 
       embedded eigenvalues /|cby Fumio Hiroshima 
264  1 Singapore :|bSpringer Singapore :|bImprint: Springer,
       |c2019 
300    1 online resource (xvi, 136 pages) :|billustrations, 
       digital ;|c24 cm 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
347    text file|bPDF|2rda 
490 1  SpringerBriefs in mathematical physics,|x2197-1757 ;
       |vvolume 35 
505 0  Introduction -- Preliminaries -- The Pauli-Fierz model -- 
       The Nelson model -- Spin-boson model -- Enhanced bindings 
520    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 
650  0 Quantum field theory 
650  0 Eigenvalues 
650 14 Mathematical Physics 
650 24 Quantum Field Theories, String Theory 
650 24 Functional Analysis 
710 2  SpringerLink (Online service) 
773 0  |tSpringer Nature eBook 
830  0 SpringerBriefs in mathematical physics ;|vvolume 35 
856 40 |uhttps://doi.org/10.1007/978-981-32-9305-2