Abelian Chern–Simons theory. I. A topological quantum field theory
Abelian Chern–Simons theory. I. A topological quantum field theory
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阿贝尔陈-西蒙斯理论。 I. 拓扑量子场论。
DOI：
10.1063/1.532333
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发表时间：
1996
影响因子：
1.3
通讯作者：
M. Manoliu
中科院分区：
文献类型：
--
作者：
M. Manoliu
本文从2+1维拓扑量子场论的观点给出了阿贝尔Chern-Simons规范理论的一个构造。量子理论的定义依赖于几何量子化思想，这些思想以前已经在非阿贝尔的陈-西蒙斯理论中进行了探索[J. Diff. 33，787-902（1991）; Topology 32，509-529（1993）]。我们制定的拓扑量子场论的扩展2-和3-流形在预印本中介绍的步行者在1991年，并证明它满足公理的酉拓扑量子场论制定的Atiyah [出版。Pans 68，175-186（1989）]。
We give a construction of the Abelian Chern–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–Simons theory [J. Diff. Geom. 33, 787–902 (1991); Topology 32, 509–529 (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 68, 175–186 (1989)].