The algebraic structure of BRST operators and their applications

This book has three related but distinct parts. In
the first part of the book, 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. In particular, for an important
class of physical theories, we show that in fact the
differential is a Chevalley-Eilenberg differential.
In the second part of the book, 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.
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.

Autorentext

Jining Gao got his Ph. D in 2005 under the direction of professor R. Fulp at North Carolina State University . His major research focuses on cohomology physics, quantum deformation theory, Mirror symmetry.

Klappentext

This book has three related but distinct parts. In the first part of the book, we construct a new sequence of generators of the BRSTcomplex 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. In particular, for an important class of physical theories, we show that in fact the differential is a Chevalley-Eilenberg differential. In the second part of the book, 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 generalizationsof ordinary algebraic extensions of Lie algebras. Applications of our theory provide a new constructive approach to BRST theorieswhich only contains three terms.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.