$\hat{Q}$ operator for canonical quantum gravity

Abstract

We study the properties of $\hat{Q}[\omega ]$ operator on the kinematical Hilbert space $\mathcal{H}$ for canonical quantum gravity. Its complete spectrum with respect to the spin network basis is obtained. It turns out that $\hat{Q}[\omega ]$ is diagonalized in this basis, and it is a well defined self-adjoint operator on $\mathcal{H}$. The same conclusions are also tenable on the SU(2) gauge invariant Hilbert space with the gauge invariant spin network basis.

10 pages, minor modefication, reference updated

References in corpus (1)

• Classical Geometry from a Physical State in Canonical Quantum Gravity

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