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We start from the Einstein-Hilbert action for the gravitational field in thepresence of a "point particle" source, and cast the action into thecorresponding phase space form. The dynamical variables of such a systemsatisfy the point particle mass shell constraint, the Hamilton and the momentumconstraints of the canonical gravity. In the quantized theory, thoseconstraints become operators that annihilate a state. A state can berepresented by a wave functional $\Psi$ that simultaneously satisfies theKlein-Gordon and the Wheeler-DeWitt-Schr\"odinger equation. The latterequation, besides the term due to gravity, also contains the Schr\"odinger liketerm, namely the derivative of $\Psi$ with respect to time, that occurs becauseof the presence of the point particle. The particle's time coordinate, $X^0$,serves the role of time. Next, we generalize the system to $p$-branes, and findout that for a quantized spacetime filling brane there occurs an effectivecosmological constant, proportional to the expectation value of the brane'smomentum, a degree of freedom that has two discrete values only, a positive anda negative one. This mechanism could be an explanation for the smallcosmological constant that drives the accelerated expansion of the universe.

Klein-Gordon-Wheeler-DeWitt-Schroedinger Equation