Direct Sum Decompositions and Indecomposable TQFT's

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 decompose into a sum of theories in which the Hilbert space of the sphere is one-dimensional, and indecomposable two-dimensional theories are classified.Comment: 10 pages, AMSLaTeX, 5 figures compressed and uuencoded by uufile

Path Integration in Two-Dimensional Toplogical Quantum Field Theory

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 generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure, give the two-dimensional axiomatic topological quantum field theories, or TQFT's, in terms of which Durhuus and Jonsson decompose every two-dimensional unitary TQFT as a direct sum.Comment: 13 pages, LaTeX with amsfonts and psfig, 3 postscript figures and .bbl file tar'd and compressed by uufile