Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary

Abstract

We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries in any dimension. The quantization proceeds in two steps. First, the classical theory is encoded into an axiomatic form describing solution spaces associated to manifolds. Second, the quantum theory is constructed from the classical axiomatic data in a functorial manner. The target is general boundary quantum field theory, a TQFT-type axiomatic formulation of quantum field theory.

References in corpus (11)

• Global Aspects of Electric-Magnetic Duality
• General boundary quantum field theory: Foundations and probability interpretation
• Perturbative quantum gauge theories on manifolds with boundary
• Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation
• Affine holomorphic quantization
• Two-dimensional quantum Yang-Mills theory with corners
• Semiclassical quantization of classical field theories
• Schrödinger-Feynman quantization and composition of observables in general boundary quantum field theory
• Free Fermi and Bose Fields in TQFT and GBF
• General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners
• Dirichlet to Neumann operator for abelian Yang-Mills gauge fields

Cited by in corpus (2)

• Locality and General Vacua in Quantum Field Theory
• The vacuum as a Lagrangian subspace