Instanton representation of Plebanski gravity: XVI. Hamiltonian and Hamilton--Jacobi dynamics on superspace

Details Instanton representation of Plebanski gravity: XVI. Hamiltonian and Hamilton--Jacobi dynamics on superspace Instanton representation of Plebanski gravity: XVI. Hamiltonian and Hamilton--Jacobi dynamics on superspace

2008-05-26

arxiv.org/abs/0805.3760v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages. Background material for revised journal article

Scientific paper

In this paper we focus on the Hamiltonian dynamics on the kinematic phase space of the instanton representation, in the full theory. The general solutions for pure gravity are reduced to quadratures and fixed point iteration both for vanishing and nonvanishing cosmological constant, with convenient physical interpretations. A Hamilton--Jacobi analysis is performed of the semiclassical orbits and their relation to the quantum theory motivated. We have constructed Hamilton--Jacobi functionals mimicking the classical dynamics. A main result is emergence of a natural time variable on the configuration space with respect to which the remaining variables evolve.

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