Overview
- Is a comprehensive survey of recent results of the existence of ground states of models in quantum field theory
- Focuses on non-perturbative methods, independent of coupling constants and other factors
- Begins with fundamentals of quantum field theory and takes the reader to a higher level of appreciation of that theory
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 35)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Ground States of Quantum Field Models
Book Subtitle: Perturbation of Embedded Eigenvalues
Authors: Fumio Hiroshima
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-981-32-9305-2
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2019
Softcover ISBN: 978-981-32-9304-5Published: 28 August 2019
eBook ISBN: 978-981-32-9305-2Published: 16 August 2019
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: XVI, 136
Number of Illustrations: 14 b/w illustrations
Topics: Mathematical Physics, Quantum Field Theories, String Theory, Functional Analysis