The Concept of Particle Weights in Local Quantum Field Theory

by Martin Porrmann
Doctoral thesis
Date of Examination:2000-01-26
Date of issue:2001-10-31
Referee:Prof. Dr. Detlef Buchholz
Referee:Prof. Dr. Klaus Fredenhagen
Persistent Address: http://dx.doi.org/10.53846/goediss-2098

 

 

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Abstract

English

Within the framework of Wigner's theory, the concept of particles in attached to irreducible unitary representations of the Poincare group, characterized by the parameters m(mass) and s (spin). However, in theories with long-range interactions the Lorentz symmetry is broken so that this apporach is no longer applicable, a phenomenon known under the term 'infraparticle problem'. Local Quantum Physics constitutes the setting for a unified treatment of both particles and infraparticles via the concept of particle weights. These arise as temporal limits of physical states in the vacuum sector and describe the asymptotic particle content. Following a thorough analysis of the underlying notion of localizing operators, we give a precise definition of the concept and investigate the characteristic properties. The decomposition of particle weights into pure components which are linked to irreducible representations of the quasi-local algebra has been a long-standing desideratum. We set! out two apporaches to this problem : First, a spatial disintegration of the representation pertaining to a particle weight in terms of irreducible ones is constructed, where it turns out to be necessary to implement certain separability conditions. Secondly, according to Choquet's theory, a barycentric decomposition with respect to the positiv cone of all particle weights is presented on the basis of topological considerations. These require a physically motivated assumption concerning the phase space of quantum field theory (compactness condition), which likewise is used to establish local normality of the representations arising in the course of the first construction, thus demonstrating that the necessary separability conditions to be met in this case do not entail a loss of essential information. The significance of the pure particle weights ensuing from this disintegration is founded on the fact that they exhibit features of improper energy-momentum eigenstates, analogou! s to Dirac's conception, and permit a consistent definition of mass and spin even in an infraparticle situation.
 
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