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An approach to the quantization of gravity in the presence matter is examinedwhich starts from the classical Einstein-Hilbert action and matter approximatedby "point" particles minimally coupled to the metric. Upon quantization, theHamilton constraint assumes the form of the Schr\"odinger equation: it containsthe usual Wheeler-DeWitt term and the term with the time derivative of the wavefunction. In addition, the wave function also satisfies the Klein-Gordonequation, which arises as the quantum counterpart of the constraint amongparticles' momenta. Comparison of the novel approach with the usual one inwhich matter is represented by scalar fields is performed, and shown that thoseapproaches do not exclude, but complement each other. In final discussion it ispointed out that the classical matter could consist of superparticles orspinning particles, described by the commuting and anticommuting Grassmanncoordinates, in which case spinor fields would occur after quantization.

A Novel Approach to Quantum Gravity in the Presence of Matter without the Problem of Time