Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 105, 31 pages      arXiv:1712.05537      https://doi.org/10.3842/SIGMA.2018.105

Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary

Homero G. Díaz-Marín a and Robert Oeckl b
a) Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, C.P. 58060, Morelia, Michoacán, Mexico
b) Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58190, Morelia, Michoacán, Mexico

Received December 18, 2017, in final form September 18, 2018; Published online September 27, 2018

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.

Key words: Yang-Mills theory; TQFT; Riemannian manifolds.

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