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The stack of Yang-Mills fields on Lorentzian manifolds

Benini, Marco; Schenkel, Alexander; Schreiber, Urs

Authors

Marco Benini

Urs Schreiber



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.

Citation

Benini, M., Schenkel, A., & Schreiber, U. (2018). The stack of Yang-Mills fields on Lorentzian manifolds. Communications in Mathematical Physics, 359(2), 765-820. https://doi.org/10.1007/s00220-018-3120-1

Journal Article Type Article
Acceptance Date Jan 19, 2018
Online Publication Date Mar 21, 2018
Publication Date 2018-04
Deposit Date Mar 14, 2018
Publicly Available Date Mar 29, 2024
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 359
Issue 2
Pages 765-820
DOI https://doi.org/10.1007/s00220-018-3120-1
Keywords Yang-Mills theory, globally hyperbolic Lorentzian manifolds, Cauchy problem, stacks, presheaves of groupoids, homotopical algebra, model categories
Public URL https://nottingham-repository.worktribe.com/output/929337
Publisher URL https://link.springer.com/article/10.1007%2Fs00220-018-3120-1
Additional Information Received: 12 April 2017; Accepted: 19 January 2018; First Online: 21 March 2018

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