The stack of Yang-Mills fields on Lorentzian manifolds
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 parametriz...
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/50439/ |
| _version_ | 1848798251597168640 |
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| author | Benini, Marco Schenkel, Alexander Schreiber, Urs |
| author_facet | Benini, Marco Schenkel, Alexander Schreiber, Urs |
| author_sort | Benini, Marco |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:16:48Z |
| format | Article |
| id | nottingham-50439 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:16:48Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-504392020-05-04T19:34:09Z https://eprints.nottingham.ac.uk/50439/ The stack of Yang-Mills fields on Lorentzian manifolds Benini, Marco Schenkel, Alexander Schreiber, Urs 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. Springer 2018-04-30 Article PeerReviewed Benini, Marco, 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 Yang-Mills theory globally hyperbolic Lorentzian manifolds Cauchy problem stacks presheaves of groupoids homotopical algebra model categories https://link.springer.com/article/10.1007%2Fs00220-018-3120-1 doi:10.1007/s00220-018-3120-1 doi:10.1007/s00220-018-3120-1 |
| spellingShingle | Yang-Mills theory globally hyperbolic Lorentzian manifolds Cauchy problem stacks presheaves of groupoids homotopical algebra model categories Benini, Marco Schenkel, Alexander Schreiber, Urs The stack of Yang-Mills fields on Lorentzian manifolds |
| title | The stack of Yang-Mills fields on Lorentzian manifolds |
| title_full | The stack of Yang-Mills fields on Lorentzian manifolds |
| title_fullStr | The stack of Yang-Mills fields on Lorentzian manifolds |
| title_full_unstemmed | The stack of Yang-Mills fields on Lorentzian manifolds |
| title_short | The stack of Yang-Mills fields on Lorentzian manifolds |
| title_sort | stack of yang-mills fields on lorentzian manifolds |
| topic | Yang-Mills theory globally hyperbolic Lorentzian manifolds Cauchy problem stacks presheaves of groupoids homotopical algebra model categories |
| url | https://eprints.nottingham.ac.uk/50439/ https://eprints.nottingham.ac.uk/50439/ https://eprints.nottingham.ac.uk/50439/ |