2019/03/19 by Merced Montesinos, Jorge Romero, Mariano Celada
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Class (philosophy) #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Covariant transformation #Gauge (firearms) #Gauge theory #General relativity #Lorentz transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Symplectic geometry #Theoretical physics #Transformation (genetics) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.99.064029
published as Phys. Rev. D 99, 064029 (2019) · It matches published version
openalex publication_date 2019/03/19 · arxiv created 2019/03/21 · arxiv updated 2019/03/25 · openalex created_date 2019/04/01 · openalex updated_date 2026/08/05
In this paper we revisit the nonmanifestly Lorentz-covariant canonical analysis of the Holst action with a cosmological constant. We take a viewpoint close to that of F. Cianfrani and G. Montani [Phys. Rev. Lett. 102, 091301 (2009)] and realize that the solution of the second-class constraints that the authors provide is incomplete, thus not accounting for the correct local dynamics of general relativity. We then mend their approach by adding the missing degrees of freedom to the solution and give a complete description of the resulting theory, which preserves Lorentz invariance but turns out to be endowed with a noncanonical symplectic structure. Later on and without resorting to any gauge condition, we perform a Darboux transformation to bring this theory into a canonical form. Finally, we show that in the time gauge both formulations, namely the noncanonical and the canonical ones, lead to the Ashtekar-Barbero variables.