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.
|Titolo:||The Stack of Yang-Mills Fields on Lorentzian Manifolds|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||01.01 - Articolo su rivista|
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|arXiv 1704.01378v2 [math-ph] 23032018.pdf||Pre-print||Open Access Visualizza/Apri|
|Benini2018_Article_TheStackOfYangMillsFieldsOnLor.pdf||Versione editoriale||Open Access Visualizza/Apri|