Preliminaries

研究成果: Chapter in Book/Report/Conference proceedingChapter

抄録

In this chapter we introduce fundamental tools used throughout this book. Compact operators on Banach spaces and compact embeddings of Sobolev spaces of the form (Formula presented) are reviewed, which can be applied to study perturbations of eigenvalues embedded in the continuous spectrum of selfadjoint operators which describe Hamiltonians in quantum field theory. The boson Fock space F(W) over Hilbert space W is defined. Creation operators a(f), annihilation operators (Formula presented), second quantization Γ (T) and differential second quantization dΓ (h) are introduced as operators in F(W). We also define operator dΓ (k, h) being an extension of dΓ (h) and discuss localizations in F(W) via the canonical identification (Formula presented). Finally we review compact operators of the form (Formula presented) in (Formula presented) and (Formula presented) in (Formula presented), and demonstrate their applications.

本文言語英語
ホスト出版物のタイトルSpringerBriefs in Mathematical Physics
出版社Springer
ページ15-40
ページ数26
DOI
出版ステータス出版済み - 1 1 2019

出版物シリーズ

名前SpringerBriefs in Mathematical Physics
35
ISSN(印刷版)2197-1757
ISSN(電子版)2197-1765

All Science Journal Classification (ASJC) codes

  • 数理物理学
  • 物理学および天文学(その他)

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