# The stack of Yang-Mills fields on Lorentzian manifolds

#### Autoren: Marco Benini, Alexander Schenkel, Urs Schreiber (2018)

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 BGcon.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
765-820
Band:
359, no. 2

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