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 BG con .
The Stack of Yang–Mills Fields on Lorentzian Manifolds / Benini, Marco; Schenkel, Alexander; Schreiber, Urs. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 359:2(2018), pp. 765-820. [10.1007/s00220-018-3120-1]
The Stack of Yang–Mills Fields on Lorentzian Manifolds
Schenkel, Alexander
;
2018-01-01
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 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 BG con .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
