The Algebraic Structure of BRST Operators and their Applications

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dc.contributor.advisor Ronald. Fulp, Committee Chair en_US Gao, Jining en_US 2010-04-02T19:09:06Z 2010-04-02T19:09:06Z 2005-10-18 en_US
dc.identifier.other etd-05192005-172803 en_US
dc.description.abstract This dissertation has two related but distinct parts. In the first part of the thesis, we construct a new sequence of generators of the BRST complex and reformulate the BRST differential so that it acts on elements of the complex much like the Maurer-Cartan differential acts on left-invariant forms. Thus our BRST differential is formally analogous to the differential defined on the BRST formulation of the Chevalley-Eilenberg cochain complex of a Lie algebra. Moreover, for an important class of physical theories, we show that in fact the differential is a Chevalley-Eilenberg differential. As one of the applications of our formalism, we show that the BRST differential provides a mechanism which permits us to extend a nonintegrable system of vector fields on a manifold to an integrable system on an extended manifold. In the second part of the thesis, we isolate a new concept which we call the chain extension of a $D$-algebra. We demonstrate that this idea is central to to a number of applications to algebra and physics. Chain extensions may be regarded as generalizations of ordinary algebraic extensions of Lie algebras. Applications of our theory provide a new constructive approach to BRST theories which only contains three terms; in particular, this provides a new point of view concerning consistent deformations and constrained Hamiltonian systems. Finally, we show that a similar development provides a method by which Lie algebra deformations may be encoded into the structure maps of an sh-Lie algebra with three terms. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject gauge symmetry en_US
dc.subject BRST dufferential en_US
dc.title The Algebraic Structure of BRST Operators and their Applications en_US PhD en_US dissertation en_US Mathematics en_US

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