Topics in the theory of lie fields

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Lowenstein, John Hood

Contributors dc:contributor

• Haag, R.

• Lie fields
• inhomogeneous Lorentz invariance
• scalar Lie field
• quantum mechanics
• many-body systems

Statement dc:rights

• 1966 John Hood Lowenstein

Language dc:language

en

Identifier

6132895

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/25051