A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter
| dc.creator | Randono, Andrew | |
| dc.date | 2005-04-02 | |
| dc.date.accessioned | 2026-07-07T03:29:31Z | |
| dc.date.available | 2026-07-07T03:29:31Z | |
| dc.description | The Kodama State for Lorentzian gravity presupposes a particular value for the Immirzi-parameter, namely $β=-i$. 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 $β$. Thus, we present an extension of the Kodama state for arbitrary values of the Immirzi parameter, $β$, that reduces to the ordinary Chern-Simons state for the particular value $β=-i$. The state for real values of $β$ 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 $β$, 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 $β$ that allows one to use the simpler self-dual and anti-self-dual forms of the constraint as an intermediate step. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0504010 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0504010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/35247 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | A Generalization of the Kodama State for Arbitrary Values of the Immirzi Parameter | |
| dc.type | text |