Groupoids of Connections and Higher-Algebraic QFT

          @misc{ pirsa_PIRSA:09050041,
            doi = {10.48660/09050041},
            url = {https://pirsa.org/09050041},
            author = {Morton, Jeffrey},
            keywords = {},
            language = {en},
            title = {Groupoids of Connections and Higher-Algebraic QFT},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {may},
            note = {PIRSA:09050041 see, \url{https://pirsa.org}}
          }
          

Abstract

This talk will discuss, illustrated by a toy example, how to construct "higher-algebraic" quantum field theories using groupoids. In particular, the groupoids describe configuration spaces of connections, together with their gauge symmetries, on spacetime, space, and boundaries of regions in space. The talk will describe a higher-algebraic "sum over histories", and how this construction is related to usual QFT's, and particularly the relation to the case of the Chern-Simons theory.