2012/05/28 by Bianca Dittrich · 91 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Discretization #Embedding #Granularity #Mathematical analysis #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Renormalization #Statistical physics #Theoretical physics #gr-qc #hep-lat #quant-ph
paper · pdf · doi:10.1088/1367-2630/14/12/123004
published in New Journal of Physics 14(12), 123004 (IOP Publishing) · 22 pages
arxiv created 2012/05/28 · openalex publication_date 2012/12/07 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations exactly mirror the continuum limit. As a standard tool for the kinematics of loop quantum gravity, we propose a coarse-graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse-graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme for this purpose. A crucial role in this coarse-graining scheme is played by the embedding maps that allow interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as the choice of embedding maps will determine the truncation of the renormalization flow.