PIRSA:23030107

Video URL

https://pirsa.org/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 for Theoretical Physics. https://pirsa.org/23030107

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

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2023},
            month = {mar},
            note = {PIRSA:23030107 see, \url{https://scivideos.org/pirsa/23030107}}
          }

Thomas Thiemann University of Erlangen-Nuremberg

Talk numberPIRSA:23030107
DOI10.48660/23030107
Source RepositoryPIRSA
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