2017/09/30 by Christoph Charles · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Degenerate energy levels #Euclidean quantum gravity #Immirzi parameter #Loop quantum cosmology #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum algorithm #Quantum gravity #Quantum mechanics #Spin foam #Theoretical physics #gr-qc
paper · pdf · doi:10.1103/physrevd.97.106002
published in Physical review. D/Physical review. D. 97(10) (American Physical Society) · 24 pages, figures in tikz
arxiv created 2017/11/27 · openalex publication_date 2018/05/03 · arxiv updated 2018/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In loop quantum gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity constraints. Their geometrical interpretation is however unsatisfactory as they do not constitute a space-time connection. It would be possible to resolve this point by using a full Lorentz connection or, equivalently, by using the self-dual Ashtekar variables. This leads however to simplicity constraints or reality conditions which are notoriously difficult to implement in the quantum theory. We explore in this paper the possibility of using completely degenerate actions to impose such constraints at the quantum level in the context of canonical quantization. To do so, we define a simpler model, in 3D, with similar constraints by extending the phase space to include an independent vielbein. We define the classical model and show that a precise quantum theory by gauge unfixing can be defined out of it, completely equivalent to the standard 3D Euclidean quantum gravity. We discuss possible future explorations around this model as it could help as a stepping stone to define full-fledged covariant loop quantum gravity.