Abstract: |
In order to set up a theory of quantization for field theories, we would like to choose a category whose objects describe, for example, the structure on the moduli "space" of solutions to the field equations (possibly quotiented out by a gauge group). Here we motivate and study one possible category, the category of commutative convenient dg-algebras. That is, the category of commutative monoid objects in chain complexes of convenient vector spaces (eg. Kriegl and Michor's "The convenient setting of global analysis"), or equivalently, in chain complexes of complete bornological vector spaces (e.g. Henri Hogbe-Nlend's "Bornologies and functional analysis"). No prior knowledge of these vector spaces will be assumed. |