2010/01/20 by Alok Laddha, Madhavan Varadarajan · 2 citations
Mathematics · Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Classical limit #Classical mechanics #Linear-quadratic-Gaussian control #Loop quantum gravity #Mathematical physics #Mathematics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Scalar field #Scalar field theory #Theoretical physics #gr-qc
paper · pdf · doi:10.1088/0264-9381/27/17/175010
published as Class.Quant.Grav.27:175010,2010 · 58 pages
arxiv created 2010/01/20 · openalex publication_date 2010/07/23 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Building on prior work, a generally covariant reformulation of a free scalar field theory on the flat Lorentzian cylinder is quantized using loop quantum gravity (LQG)-type 'polymer' representations. This quantization of the continuum classical theory yields a quantum theory which lives on a discrete spacetime lattice. We explicitly construct a state in the polymer Hilbert space which reproduces the standard Fock vacuum two-point functions for long-wavelength modes of the scalar field. Our construction indicates that the continuum classical theory emerges under coarse graining. All our considerations are free of the 'triangulation' ambiguities which plague attempts to define quantum dynamics in LQG. Our work constitutes the first complete LQG-type quantization of a generally covariant field theory together with a semi-classical analysis of the true degrees of freedom and thus provides a perfect infinite-dimensional toy model to study open issues in LQG, particularly those pertaining to the definition of quantum dynamics.