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