Abelian Chern{endash}Simons theory. I. A topological quantum field theory
- Department of Mathematics, University of Texas, Austin, Texas 78712 (United States)
We give a construction of the Abelian Chern{endash}Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern{endash}Simons theory [J. Diff. Geom. {bold 33}, 787{endash}902 (1991); Topology {bold 32}, 509{endash}529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans {bold 68}, 175{endash}186 (1989)]. {copyright} {ital 1998 American Institute of Physics.}
- OSTI ID:
- 565706
- Journal Information:
- Journal of Mathematical Physics, Vol. 39, Issue 1; Other Information: PBD: Jan 1998
- Country of Publication:
- United States
- Language:
- English
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