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arXiv 1912.11202math-phhep-thmath.MP
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二维微扰标量QFT与Atiyah-Segal胶合

Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing

Santosh Kandel, Pavel Mnev, Konstantin Wernli

备注：
V.2: numerous expository changes; typos corrected. New additions: an analysis of singularities of boundary states induced from Feynman diagrams (sec. 3); a second (perturbative) proof of functoriality (sec. 7); new examples added in Appendix A.2.3, A.3.3 and a new general result on Dirichlet-to-Neumann operators in A.3.3; a new result on trace anomaly in Appendix B. V.3: typos corrected
发表信息：
Advances in Theoretical and Mathematical Physics 25, no. 7 (2021): 1847-1952
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摘要：

研究了具有多项式（或幂级数）势的二维有质量标量场理论在有边界流形上的微扰量子化。我们证明它符合Atiyah-Segal的函子量子场论框架。特别地，我们证明了根据曲面上点的配置空间上的积分定义的微扰配分函数满足Atiyah-Segal型胶合公式。蝌蚪（短环）在胶合作用下表现得很不寻常，并在结果中起着至关重要的作用。

英文摘要：

We study the perturbative quantization of 2-dimensional massive scalar field theory with polynomial (or power series) potential on manifolds with boundary. We prove that it fits into the functorial quantum field theory framework of Atiyah-Segal. In particular, we prove that the perturbative partition function defined in terms of integrals over configuration spaces of points on the surface satisfies an Atiyah-Segal type gluing formula. Tadpoles (short loops) behave nontrivially under gluing and play a crucial role in the result.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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