Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-06-24
Phys.Rev.D81:064033,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Appendix added where moldels leading to boundary degrees of freedom are constructed. This version will appear in PRD.
Scientific paper
10.1103/PhysRevD.81.064033
We study the Hamiltonian formulation of the generally covariant theory defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This theory can be thought of as the limit of the Holst action for gravity for the Newton constant G goes to infinity and Immirzi parameter goes to zero, while keeping their product fixed. This theory has for a long time been conjectured to be topological. We prove this statement both in the covariant phase space formulation as well as in the standard Dirac formulation. In the time gauge, the unconstrained phase space of theory admits an SU(2) connection formulation which makes it isomorphic to the unconstrained phase space of gravity in terms of Ashtekar-Barbero variables. Among possible physical applications, we argue that the quantization of this topological theory might shed new light on the nature of the degrees of freedom that are responsible for black entropy in loop quantum gravity.
Liu Lihui
Montesinos Merced
Perez Alejandro
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