PIRSA:19120014

On geometry and symmetries in gauge gravity: Cartan connection approach

Belov, V. (2019). On geometry and symmetries in gauge gravity: Cartan connection approach. Perimeter Institute. https://pirsa.org/19120014

Belov, Vadim. On geometry and symmetries in gauge gravity: Cartan connection approach. Perimeter Institute, Dec. 10, 2019, https://pirsa.org/19120014 

          @misc{ pirsa_PIRSA:19120014,
            doi = {10.48660/19120014},
            url = {https://pirsa.org/19120014},
            author = {Belov, Vadim},
            keywords = {Quantum Gravity},
            language = {en},
            title = {On geometry and symmetries in gauge gravity: Cartan connection approach},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {dec},
            note = {PIRSA:19120014 see, \url{https://pirsa.org}}
          }

Vadim Belov Universität Hamburg

DOI 10.48660/19120014
Collection
Talk Type Scientific Series
Subject

Abstract

Our earlier findings indicate the violation of the 'volume simplicity' constraint in the current Spinfoam models (EPRL-FK-KKL). This result, and related problems in LQG, promted to revisit the metric/vielbein degrees of freedom in the classical Einstein-Cartan gravity. Notably, I address in detail what constitutes a 'geometry' and its 'group of motions' in such Poincare gauge theory. In a differential geometric scheme that I put forward the local translations are not broken but exact, and their relation to diffeomorphism transformations is clarified. The refined notion of a tensor takes into account the (relative) localization in spacetime, whereas the key concept of 'development' generalizes parallel transport (of vectors and points) to affine spaces. I advocate for this Cartan connection as the fundamental d.o.f. of the gravitational field, and discuss implications for discretization and quantization. Based on [1905.06931].