The Algebraic Structure of BRST Operators and their Applications

gauge symmetry;BRST dufferential

Gao, Jining ; Ronald. Fulp, Committee Chair,Gao, Jining ; Ronald. Fulp ; Committee Chair

University:North Carolina State University

关键词: gauge symmetry;    BRST dufferential;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5180/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

This dissertationhas 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 onthe 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 asgeneralizations of ordinary algebraic extensions of Lie algebras. Applications of our theory provide a new constructive approach toBRST 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 beencoded into the structure maps of an sh-Lie algebra with three terms.