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