FU Berlin Digitale Dissertation
Carsten Binnenhei : Ladungstragende Quantenfelder assoziiert mit Endomorphismen auf CAR- und CCR-Algebren Charged Quantum Fields Associated with Endomorphisms of CAR and CCR Algebras
|Abstract| |Table of Contents| |More Information|

Abstract The appearance of the Cuntz algebras Od is a generic feature of local quantum field theory. This fact has been discovered by S. Doplicher and J. E. Roberts within the algebraic theory of superselection sectors. Generators of the Cuntz algebras arise as charged field operators which implement localized endomorphisms of the observable algebra. Whereas the existence of such operators can be derived from first principles, little is known about the actual construction of these fields in concrete models. In view of this apparent discrepancy, we develop a comprehensive theory of quasi-free endomorphisms of the CAR and CCR algebras which give rise to representations of the Cuntz algebras Od on Fock space. The number d is the statistics dimension of the endomorphism. It can be any power of 2 (including 1 and infinite) in the CAR case, but takes only the values 1 and infinite in the CCR case. We obtain necessary and sufficient conditions for implementability of quasi-free endomorphisms. By studying extensions of partial Fock states, we find that the semigroup of implementable quasi-free endomorphisms has a simple structure: It can be written as a product of a group of automorphisms which are close to the identity, and the semigroup of endomorphisms which leave the given Fock state invariant. We describe the construction of the implementers of a quasi-free endomorphism in terms of annihilation and creation operators in is a generic feature of local quantum field theory. This fact has been discovered by S. Doplicher and J. E. Roberts within the algebraic theory of superselection sectors. Generators of the Cuntz algebras arise as charged field operators which implement localized endomorphisms of the observable algebra. Whereas the existence of such operators can be derived from first principles, little is known about the actual construction of these fields in concrete models. We compare the structure of the semigroup of (gauge invariant) quasi-free endomorphisms with the generic superselection structure of quantum field theory.

Table of Contents Download the whole PhDthesis as a zip-tar file or as zip-File For download in PDF format click the chapter title Cover and Contents Introduction The Algebraic Theory of Superselection Sectors What We Have Done Endomorphisms of CAR and CCR Algebras The Cuntz Algebras Quasi-free Endomorphisms of the CAR Algebra Quasi-free Endomorphisms of the CCR Algebra Superselection Sectors Reached by Gauge Invariant Quasi--free Endomorphisms What We Have Not Learnt Yet Bibliography

More Information:
Online available:	http://darwin.inf.fu-berlin.de/1998/11/indexe.html
Language of PhDThesis:	english
Keywords:	algebraic quantum field theory; superselection sectors; endomorphisms; CAR algebra; CCR algebra; Cuntz algebra
DNB-Sachgruppe:	29 Physik, Astronomie
Classification PACS:	11.10.Cd; 03.70.+k; 02.30.Tb
Date of disputation:	11-Jun-1998
PhDThesis from:	Fachbereich Physik, Freie Universität Berlin
First Referee:	Prof. Dr. Bert Schroer
Second Referee:	Prof. Dr. Robert Schrader
Contact (Author):	carsten.binnenhei@physik.fu-berlin.de
Contact (Advisor):	Bert.Schroer@physik.fu-berlin.de
Date created:	09-Dec-1998
Date available:	14-Dec-1998

 

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