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 [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 $\mathrm{B}{G}_{\mathrm{con}}$.

50 pages, final version published in Communications in Mathematical Physics

References in corpus (2)

• Higher Topos Theory
• Synthetic geometry of differential equations: I. Jets and comonad structure

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