The stack of Yang-Mills fields on Lorentzian manifolds

Benini, Marco and Schenkel, Alexander and Schreiber, Urs (2018) The stack of Yang-Mills fields on Lorentzian manifolds. Communications in Mathematical Physics, 359 (2). pp. 765-820. ISSN 1432-0916

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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 BGcon.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/929337
Keywords: Yang-Mills theory, globally hyperbolic Lorentzian manifolds, Cauchy problem, stacks, presheaves of groupoids, homotopical algebra, model categories
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s00220-018-3120-1
Depositing User: Eprints, Support
Date Deposited: 14 Mar 2018 11:41
Last Modified: 04 May 2020 19:34
URI: http://eprints.nottingham.ac.uk/id/eprint/50439

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