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Haag, R. Lowenstein, John Hood 2011-05-27T16:42:40Z 2011-05-27T16:42:40Z 10000-01-01 1966 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. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-27T16:42:40Z No. of bitstreams: 1 1966_lowenstein.pdf: 2773508 bytes, checksum: a80558ff7c1f5c2f188ab4e56edaf0d8 (MD5) Made available in DSpace on 2011-05-27T16:42:40Z (GMT). No. of bitstreams: 1 1966_lowenstein.pdf: 2773508 bytes, checksum: a80558ff7c1f5c2f188ab4e56edaf0d8 (MD5) Previous issue date: 1966 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-27T16:42:40Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:13:46-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Thesis U of I Only 6132895 http://hdl.handle.net/2142/25051 en 1966 John Hood Lowenstein Lie fields inhomogeneous Lorentz invariance scalar Lie field quantum mechanics many-body systems Topics in the theory of lie fields Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.