Higher-Dimensional Algebra: A Language for Quantum Spacetime

          @misc{ pirsa_PIRSA:06050028,
            doi = {10.48660/06050028},
            url = {https://pirsa.org/06050028},
            author = {Baez, John},
            keywords = {Quantum Foundations, Quantum Gravity},
            language = {en},
            title = {Higher-Dimensional Algebra: A Language for Quantum Spacetime},
            publisher = {Perimeter Institute},
            year = {2006},
            month = {may},
            note = {PIRSA:06050028 see, \url{https://pirsa.org}}
          }
          

Abstract

Category theory is a general language for describing things and processes - called "objects" and "morphisms". In this language, many counterintuitive features of quantum theory turn out to be properties shared by the category of Hilbert spaces and the category of cobordisms, in which objects are choices of "space" and emorphisms are choices of "spacetime". This striking fact suggests that "n-categories with duals" are a promising language for a quantum theory of spacetime. We sketch the historical development of these ideas from Feynman diagrams to string theory, topological quantum field theory, spin networks and spin foams, and especially recent work on open-closed string theory, 3d quantum gravity coupled to point particles, and 4d BF theory coupled to strings.