PIRSA:23030107

Quantum Bergmann-Komar group, U(1)^3 quantum gravity and loop quantum gravity

Thiemann, T. (2023). Quantum Bergmann-Komar group, U(1)^3 quantum gravity and loop quantum gravity. Perimeter Institute. https://pirsa.org/23030107

Thiemann, Thomas. Quantum Bergmann-Komar group, U(1)^3 quantum gravity and loop quantum gravity. Perimeter Institute, Mar. 16, 2023, https://pirsa.org/23030107 

          @misc{ pirsa_PIRSA:23030107,
            doi = {10.48660/23030107},
            url = {https://pirsa.org/23030107},
            author = {Thiemann, Thomas},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Quantum Bergmann-Komar group, U(1)^3 quantum gravity and loop quantum gravity},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {mar},
            note = {PIRSA:23030107 see, \url{https://pirsa.org}}
          }

Thomas Thiemann University of Erlangen-Nuremberg

DOI 10.48660/23030107
Collection
Talk Type Scientific Series
Subject

Abstract

In any approach to quantum gravity, the quantum representation theory of the "algebra" of Cauchy hypersurface deformations plays a crucial role. Its faithful implementation is a key step towards constructing a valid theory of quantum gravity as it ensures quantum spacetime diffeomorphism covariance. Bergmann and Komar were the first to consider the possibilty of a corresponding quantum "group". Its construction is mathematically challenging in more than 1+1 spacetime dimensions because one leaves the realm of Lie algebras and Lie groups. After an introduction to these concepts, we show that the Bergmann Komar "group" can indeed be faithfully implemented in a weakly self-interacting truncation of 3+1 quantum gravity with two propagating polarisations. We then discuss possible implications for the actual, untruncated theory.

Zoom link:  https://pitp.zoom.us/j/91488383205?pwd=bkxGS0huMGNEYXc3Y2FJSGZHQ0pqQT09