  The trace anomaly and the cosmological constant problem are two typical
breakdowns when applying the quantum principle to a general covariant or
gravitational system. A quantum theory of spacetime reference frame is proposed
and reviewed. We study the theory by functional method, and show that the trace
anomaly of the theory is closely related to some of the Perelman's functionals.
The functionals may provide us possible links between the trace anomaly and the
cosmological constant. We find that to cancel the trace anomaly at the lab's
scale up to very high energy, a cosmological constant is required which is
consistent with observations. In the framework, an effective theory of gravity
and possible observational effect are also discussed.
