Quantum abelian Yang-Mills theory on Riemannian manifolds with boundary. (English) Zbl 1454.81142
Summary: 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.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T70 | Quantization in field theory; cohomological methods |
| 53D50 | Geometric quantization |
| 58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
| 58E30 | Variational principles in infinite-dimensional spaces |
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