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https://hdl.handle.net/2142/25051
Description
Title
Topics in the theory of lie fields
Author(s)
Lowenstein, John Hood
Issue Date
1966
Doctoral Committee Chair(s)
Haag, R.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Lie fields
inhomogeneous Lorentz invariance
scalar Lie field
quantum mechanics
many-body systems
Language
en
Abstract
In this dissertation the author discusses several
aspects of the theory of Lie fields (for which the
commutator of the field operators at two space-time
points is linear in the field, so that one has an
infinite-dimensional Lie algebra). It is shown that,
contrary to what is currently believed, the existence
of scalar Lie fields is not precluded by the algebraic
considerations of inhomogeneous Lorentz invariance and
weak locality alone. The author derives a partial
categorization of the wide variety of possible scalar
Lie field structures and presents the simplest types of
examples. A Lorentz-invariant representation of one of
these examples is obtainedo
In a later chapter, a vector Lie field associated
with the coordinate transformations of differential
geometry is discussed as the simplest example of a
Lorentz-invariant, strictly local Lie field having a
Lorentz-invariant vacuum representation.
Finally, the author discusses the possible usefulness
of Lie fields in two contexts: (a) in the
quantum-mechanical formulation of gauge invariance, and
(b) in the description of nonrelativistic many-body
systems (where,·· of course, the Lie fields are defined over
Euclidean three-space) 0 The latter provides an alternative
to the traditional equal~time formulation in terms
of fields satisfying canonical commutation or anticommutation
relations.
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