陈-西蒙斯规范理论中的费米子化和收敛微扰展开
Fermionization and Convergent Perturbation Expansions in Chern-Simons Gauge Theory
摘要：
我们证明了具有适当截断的陈-西蒙斯规范理论在微扰论中是等价于具有非定域相互作用项的费米子理论的。当在费米场上附加一个截止点时，这个费米理论产生一个收敛的微扰展开。这使我们猜想，陈-西蒙斯规范理论也产生了收敛微扰展开，这将给出一个数学上定义良好的理论结构。
英文摘要：
We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to conjecture that Chern-Simons gauge theory also gives rise to convergent perturbation expansions, which would give a mathematically well-defined construction of the theory.
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