Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing

Abstract

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.

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

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Cited by in corpus (3)

• Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions
• Dirichlet Scalar Determinants On Two-Dimensional Constant Curvature Disks
• Lorentzian bordisms in algebraic quantum field theory