TY  - JOUR
A1  - Benini, Marco
A1  - Schenkel, Alexander
T1  - Quantum Field Theories on Categories Fibered in Groupoids
T2  - Communications in mathematical physics
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.
Y1  - 2017
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/46243
SN  - 0010-3616
SN  - 1432-0916
VL  - 356
SP  - 19
EP  - 64
PB  - Springer
CY  - New York
ER  -