二维微扰标量量子场论与 Atiyah-Segal 粘合
数学物理
2022-07-15 v3 高能物理 - 理论
math.MP
摘要
我们研究具有多项式（或幂级数）势的二维有界流形上质量标量场论的微扰量子化。我们证明它符合 Atiyah-Segal 的函子量子场论框架。特别地，我们证明由曲面上点构型空间上的积分所定义的微扰配分函数满足 Atiyah-Segal 型粘合公式。蝌蚪图（短圈）在粘合下表现出非平凡行为，并在该结果中起关键作用。
引用
@article{arxiv.1912.11202,
title = {Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing},
author = {Santosh Kandel and Pavel Mnev and Konstantin Wernli},
journal= {arXiv preprint arXiv:1912.11202},
year = {2022}
}
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