On Spectral Triples in Quantum Gravity

          @misc{ scivideos_PIRSA:08050004,
            doi = {10.48660/08050004},
            url = {https://pirsa.org/08050004},
            author = {Grimstrup, Jesper},
            keywords = {Quantum Gravity},
            language = {en},
            title = {On Spectral Triples in Quantum Gravity},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2008},
            month = {may},
            note = {PIRSA:08050004 see, \url{https://scivideos.org/pirsa/08050004}}
          }
          

Abstract

This talk is concerned with the existence of spectral triples in quantum gravity. I will review the construction of a spectral triple over a functional space of connections. Here, the *-algebra is generated by holonomy loops and the Dirac type operator has the form of a global functional derivation operator. The spectral triple encodes the Poisson structure of General Relativity when formulated in terms of Ashtekars variables. Finally I will argue that the Hamiltonian of General Relativity may emerge from the construction via the requirement that inner automorphisms vanish on the vacuum sector.