PATH INTEGRATION IN TWO-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORY (2007)
Abstract. A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with...
Diffeomorphism-Invariant Spin Network States (2007)
We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P ! M is a...
A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel (2007)
In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of piecewise geodesic paths, the kernel of the time...
Three-Dimensional 2-Framed TQFTs and Surgery (1999)
The notion of 2-framed three-manifolds is defined. The category of 2-framed cobordisms is described, and used to define a 2-framed three-dimensional TQFT. Using skeletonization and special features...
Diffeomorphism-Invariant Spin Network States (1997)
We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a...
On Finiteness of Certain Vassiliev Invariants (1995)
Kauffman, Louis H., Saito, Masahico, Sawin, Stephen
The best known examples of Vassiliev invariants are the coefficients of a Jones-type polynomial expanded after exponential substitution. We show that for a given knot, the first $N$ Vassiliev...
Functional Integration on Spaces of Connections (1995)
Let $G$ be a compact connected Lie group and $P \to M$ a smooth principal $G$-bundle. Let a `cylinder function' on the space $\A$ of smooth connections on $P$ be a continuous function of the...
Links, Quantum Groups, and TQFT's (1995)
The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these...
Path Integration in Two-Dimensional Toplogical Quantum Field Theory (1995)
A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the...
Direct Sum Decompositions and Indecomposable TQFT's (1995)
The decomposition of an arbitrary axiomatic topological quantum field theory or TQFT into indecomposable theories is given. In particular, unitary TQFT's in arbitrary dimensions are shown to...
Functional Integration on Spaces of Connections
Suppose that G is a compact connected Lie group and P !M is a smooth principal G-bundle. We define a `cylinder function' on the space A of smooth connections on P to be a continuous complex...