Mathematical Physics seminar: Homotopical linear quantum Yang-Mills
Gauge fields and gauge transformations form a stack, which is a higher categorical space. In this talk I will discuss the simplest such case, linear gauge theory, which can be modelled by a chain complex. We study the derived critical locus of the linear Yang-Mills action and find that the usual shifted Poisson structure is exact on globally hyperbolic spacetimes. It therefore allows for trivializations, which are chain complex analogues of (advanced and retarded) Green's operators. These trivializations give rise to an unshifted Poisson structure which is central to quantizing the theory. We find that pleasingly the usual quantization already is compatible with quasi-isomorphisms. This is work in progress with M. Benini and A. Schenkel.