A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter

Details A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter

2005-04-02

arxiv.org/abs/gr-qc/0504010v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages

Scientific paper

The Kodama State for Lorentzian gravity presupposes a particular value for the Immirzi-parameter, namely $\beta=-i$. However, the derivation of black hole entropy in Loop Quantum Gravity suggests that the Immirzi parameter is a fixed value whose magnitude is on the order of unity but larger than one. Since the Kodama state has de-Sitter spacetime as its classical limit, to get the proper radiation temperature, the Kodama state should be extended to incorporate a more physical value for $\beta$. Thus, we present an extension of the Kodama state for arbitrary values of the Immirzi parameter, $\beta$, that reduces to the ordinary Chern-Simons state for the particular value $\beta=-i$. The state for real values of $\beta$ is free of several of the outstanding problems that cast doubts on the original Kodama state as a ground state for quantum general relativity. We show that for real values of $\beta$, the state is invariant under large gauge transformations, it is CPT invariant (but not CP invariant), and it is expected to be delta-function normalizable with respect to the kinematical inner product. To aid in the construction, we first present a general method for solving the Hamiltonian constraint for imaginary values of $\beta$ that allows one to use the simpler self-dual and anti-self-dual forms of the constraint as an intermediate step.

Affiliated with

Also associated with

No associations

Rating

A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-302026