Wheeler–DeWitt quantization for point-particles

We present the Hamiltonian formulation of a relativistic point-particle coupled to Einstein gravity and its canonical quantization \`a la Wheeler-DeWitt. In resulting quantum theory, wave functional is function particle coordinates 3-metric. It satisfies particular diffeomorphism constraint, together with Klein-Gordon-type equation. As usual in Wheeler-DeWitt time-independent. This also reflected equation, where time derivative absent. Before considering gravity, we consider coupling electromagnetism, which treated similarly, but simpler.