On the construction of macroscopically local relativistic quantum theories
Nance, Jon Roland
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https://hdl.handle.net/2142/25062
Description
Title
On the construction of macroscopically local relativistic quantum theories
Author(s)
Nance, Jon Roland
Issue Date
1966
Doctoral Committee Chair(s)
Haag, R.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
macroscopically local relativistic quantum theory
relativistic quantum theory
field theory
scattering theory
quasilocal observables
scalar boson model
Language
en
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."
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