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The Stack of Yang–Mills Fields on Lorentzian Manifolds

Abstract

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 Hollander (Isr. 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.

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Correspondence to Alexander Schenkel.

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Communicated by C. Schweigert

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Benini, M., Schenkel, A. & Schreiber, U. The Stack of Yang–Mills Fields on Lorentzian Manifolds. Commun. Math. Phys. 359, 765–820 (2018). https://doi.org/10.1007/s00220-018-3120-1

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