Communications in Mathematical Physics

, Volume 359, Issue 2, pp 765–820 | Cite as

The Stack of Yang–Mills Fields on Lorentzian Manifolds

Open Access


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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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany
  2. 2.Fachbereich MathematikUniversität HamburgHamburgGermany
  3. 3.School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  4. 4.Mathematics Institute of the AcademyPragua 1Czech Republic

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