文档介绍：arXiv: [math-ph] 20 Jan 2009
pcrlTer fAutomorphism of Theory Spectral
rusadPril tutrsin Structures Particle and Groups
e ahmtshNtrisncatihnFakult¨aten Mathematisch-Naturwissenschaftlichen der
unu il Theory Field Quantum
e er-uutUiesta uG¨ottingen -August-Universit¨at zu der
u ragn e rades des Erlangung zur
ocehJnDybalski Jan Wojciech
G¨ottingen, 2008
u Warszawa aus
oglg von vorgelegt
Dissertation
D 7
Referent: Prof. Dr. D. Buchholz
Korreferent: Prof. Dr. K. Fredenhagen
Tag der m¨undlichen Pr¨ufung:
Contents
1 Introduction 5
Particle Content in Quantum Mechanics. Spectrum of Hamiltonian . . . . . 6
Wigner’s Particle Concept and its Limitations . . . . . . . . . . . . . . . . . 6
Beyond Wigner’s Particle Concept. Arveson Spectrum . . . . . . . . . . . . 7
Detailed Theory of Arveson Spectrum in Literature . . . . . . . . . . . . . . 10
Overview of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Technical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Spectral position and Existence of Particles 17
Space Translations in Quantum Mechanics . . . . . . . . . . . . . . . . . . . 18
Space Translations in Quantum Field Theory. Spectral position . . . 20
Triviality of Point-Continuous Subspace and Existence of Particles . . . . . 26
3 Uniqueness of Spectral position and Vacuum Structure 33
Condition C♯ and Existence of Vacuum States . . . . . . . . . . . . . . . . . 34
Condition C♯: Coincidence Measurement Formulation . . . . . . . . . . . . 38
Condition C♭ and Uniqueness of Vacuum . . . . . . . . . . . . . . . . . . . 42
Condition C♮: Additivity of Energy . . . . . . . . . . . . . . . . . . . . . . . 48
Condition N♮ implies Condition C♮. . . . . . . . . . . . . . . . . . . . . . . 53
4 Conclusions and Outlook 59
A Haag-Ruelle Scattering Theory in Presence of Massless Particles 63
In