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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
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 the-theory 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 creation-destruction 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
Rights Information:1966 Jon Roland Nance
Date Available in IDEALS:2011-05-31
Identifier in Online Catalog:6128057

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