# The stack of Yang-Mills fields on Lorentzian manifolds

April 05, 2017

We provide an abstract definition and an explicit construction of the stack
of non-Abelian Yang-Mills fields on globally hyperbolic Lorentzian manifolds.
We also formulate a stacky version of the Yang-Mills Cauchy problem and show
that its well-posedness is equivalent to a whole family of parametrized PDE
problems. Our work is based on the homotopy theoretical approach to stacks
proposed in [S. Hollander, Israel J. Math. 163, 93-124 (2008)], which we shall
extend by further constructions that are relevant for our purposes. In
particular, we will clarify the concretification of mapping stacks to
classifying stacks such as $\mathrm{B}G_\mathrm{con}$.

open access link
Commun. Math. Phys. (2018)

%%% contains utf-8, see: http://inspirehep.net/info/faq/general#utf8
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@article{Benini:2017zjv,
author = "Benini, Marco and Schenkel, Alexander and Schreiber, Urs",
title = "{The Stack of Yangâ€“Mills Fields on Lorentzian
Manifolds}",
journal = "Commun. Math. Phys.",
volume = "359",
year = "2018",
number = "2",
pages = "765-820",
doi = "10.1007/s00220-018-3120-1",
eprint = "1704.01378",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1704.01378;%%"
}

Keywords:

Yang-Mills theory, globally hyperbolic Lorentzian manifolds, Cauchy problem, stacks, presheaves of groupoids, homotopical algebra, model categories