On Semi-classical States of Quantum Gravity and Noncommutative Geometry

          @misc{ pirsa_PIRSA:09100143,
            doi = {10.48660/09100143},
            url = {https://pirsa.org/09100143},
            author = {Grimstrup, Jesper},
            keywords = {Quantum Gravity},
            language = {en},
            title = {On Semi-classical States of Quantum Gravity and Noncommutative Geometry},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {oct},
            note = {PIRSA:09100143 see, \url{https://pirsa.org}}
          }
          

Abstract

The idea behind an intersection between loop quantum gravity and noncommutative geometry is to combine elements of unification with a setup of canonical quantum gravity. In my talk I will first review the construction of a semi-finite spectral triple build over an algebra of holonomy loops. Here, the loop algebra is a noncommutative algebra of functions over a configurations space of connections, and the interaction between the Dirac type operator and the loop algebra captures information of the kinematical part of canonical quantum gravity. Next, I will show how certain normalizable, semi-classical states are build which connects the spectral triple construction to the Dirac Hamiltonian in 3+1 dimensions. Thus, these states can be interpreted as one-particle fermion states in an ambient gravitational field. This analysis indicates that the spectral triple construction involves matter degrees of freedom.