Revisiting the solution of the second-class constraints of the Holst action
arXiv:1903.09201 · doi:10.1103/PhysRevD.99.064029
Abstract
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.
arXiv commentIt matches published version
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- Euclidean self-dual gravity: Ashtekar variables without gauge fixing
- Linking the ADM formulation to other Hamiltonian formulations of general relativity
- The Scalar Mach-Sciama Theory of Gravitation