TY  - GEN
A1  - Benini, Marco
A1  - Schenkel, Alexander
T1  - Quantum field theories on categories fibered in groupoids
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 895 
KW  - C-asterisk-algebra
KW  - observables
KW  - covariance
KW  - locality
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-431541
SN  - 1866-8372
IS  - 895
ER  - 
TY  - JOUR
A1  - Benini, Marco
A1  - Schenkel, Alexander
A1  - Schreiber, Urs
T1  - The Stack of Yang-Mills Fields on Lorentzian Manifolds
JF  - Communications in mathematical physics
N2  - 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).
Y1  - 2018
U6  - https://doi.org/10.1007/s00220-018-3120-1
SN  - 0010-3616
SN  - 1432-0916
VL  - 359
IS  - 2
SP  - 765
EP  - 820
PB  - Springer
CY  - New York
ER  -