2011/11/30 by Steffen Gielen, Derek K. Wise · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #CPT symmetry #Classical mechanics #Cosmology and Gravitation Theories #Gauge theory #General covariance #General relativity #Hamiltonian (control theory) #Loop quantum gravity #Lorentz covariance #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Spacetime #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.85.104013
published as Phys. Rev. D 85, 104013 (2012) · 10 pages, revtex, APS style; v2: extended discussion of relation to approaches using second class constraints in abstract/introduction, made some additional small corrections; v3: fixed abstract; v4: minimal changes to match published version
openalex publication_date 2012/05/08 · arxiv created 2012/05/10 · arxiv updated 2012/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In Ashtekar's Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields, presenting a significant obstacle to quantization, or additional (usually second class) constraints whose solution renders the resulting phase space variables harder to interpret in a spacetime picture. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation in which second class constraints never arise. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3, 1) symmetry down to a subgroup SO(3)y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as ``Cartan geometrodynamics.'' We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3, 1) to SO(3) is not in conflict with Lorentz covariance.