2021/05/31 by Steffen Gielen · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Canonical quantization #Classical mechanics #Cosmology and Gravitation Theories #Geometric quantization #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #Physics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Scalar field #Second quantization #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.104.106011
published in Physical review. D/Physical review. D. 104(10) (American Physical Society) · 17 pages, revtex two-column style; v2: extended discussion, minor typographical changes, updated references; version accepted in Physical Review D; v3: corrected a few typos, changed title to match journal publication title
arxiv created 2021/11/03 · openalex publication_date 2021/11/16 · arxiv updated 2021/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Canonical quantization of gravitational systems is obstructed by the problem of time. Due to diffeomorphism symmetry the Hamiltonian vanishes: dynamics with respect to a background time parameter appears ``frozen.'' Two strategies towards the quantization of such systems are the identification of a clock degree of freedom before quantization (deparametrization), and quantization on a kinematical Hilbert space which is subject to constraints (Dirac quantization). The usual canonical quantization in quantum field theory is analogous to deparametrization. Here we introduce a frozen formalism and Dirac quantization for a complex Klein--Gordon scalar field, and show that the resulting theory is equivalent to usual canonical quantization. We then apply the formalism to the group field theory formalism for quantum gravity, for which both deparametrization and a ``timeless'' quantization have been proposed in past work. We show how a frozen formalism for group field theory links between these two existing approaches, and illustrate in particular the construction of physical observables. We derive effective cosmological dynamics for group field theory in the new formalism and compare these to previous work. The frozen formalism could be extended to other approaches to quantum gravity that do not use a preferred time parameter.