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Title:  On the construction of macroscopically local relativistic quantum theories 
Author(s):  Nance, Jon Roland 
Doctoral Committee Chair(s):  Haag, R. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  macroscopically local relativistic quantum theory
relativistic quantum theory field theory scattering theory quasilocal observables scalar boson model 
Abstract:  The problem of providing a physical interpretation of a relativistic quantum theory is discussed. It is shown that a single operator corresponding to a localized measurement on the states of thetheory is sufficient for a significant part (perhaps all) of this interpretation. The application of this method of interpretation to the relativistic quantum theory defined on the representation space of an irreducible representation of a higher symmetry group containing the Poincare group is discussed. It is concluded that the higher symmetry is, in fact, of little use for this interpretation. This .leads in a natural way to the problem of finding some of these "quasilocal" operators on the space of states of a given relativistic quantum theory. 1'/ This problem is specialized to the problem of constructing a model relativistic quantum theory of a certain type. The procedure used is to attempt to construct a representation of the generators of the Poincare group on the Fock space X of real scalarbosons in such a way that quasilocal observables are easily expressible in terms of the canonical creationdestruction operators. The structure of the model permits the construction of the generators to be approached by successively satisfying their structure relations in each of the spaces ~(n) specified by the eigenvalues of the free field particle number operator. These structure relations are satisfied in~(l) and~(2). The mathematical details of the problem increase rapidly with n, and no explicit solution is obtained for n > 2. Arguments are given which make it plausible that the structure relations in~(n), with n> 2, may be satisfied by a large class of generators. Several trial solutions in the space ~(3) are described, and the difficulties associated with them are discussed. 
Issue Date:  1966 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/25062 
Rights Information:  1966 Jon Roland Nance 
Date Available in IDEALS:  20110531 
Identifier in Online Catalog:  6128057 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois