Two-dimensional quantum Yang-Mills theory with corners

Abstract

The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds is well known. We bring this solution into a TQFT-like form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is flexible enough to capture actual quantum field theories also in higher dimensions. We motivate this axiomatic system from a formal Schroedinger-Feynman quantization procedure. We also discuss the physical meaning of unitarity, the concept of vacuum, (partial) Wilson loops and non-orientable surfaces.

31 pages, 6 figures, LaTeX + AMS; minor corrections, reference updated

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Cited by in corpus (18)

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• Observables in the General Boundary Formulation
• States and amplitudes for finite regions in a two-dimensional Euclidean quantum field theory
• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Free Fermi and Bose Fields in TQFT and GBF
• The Unruh Effect in General Boundary Quantum Field Theory
• Locality and General Vacua in Quantum Field Theory
• Quantum field theory on timelike hypersurfaces in Rindler space
• Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary
• Towards state locality in quantum field theory: free fermions
• The S-matrix in Schrödinger Representation for Curved Spacetimes in General Boundary Quantum Field Theory
• General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners
• Dirichlet to Neumann operator for abelian Yang-Mills gauge fields
• The Unruh-deWitt Detector and the Vacuum in the General Boundary formalism
• Compositional Quantum Field Theory: An axiomatic presentation