Quantum mechanics in Riemannian space-times. II: Field-theoretical approach (Q1576105)

A generally covariant formula of quantum mechanics of a neutral spinless point-like particle in the general Riemannian space-time \(V_{1,3}\) is developed in the normal geodesic frame of reference, starting from the general notions of quantum field theory in \(V_{1,3}\). A particle-interpreted Fock space is specified through the definition of the one-particle subspace asymptotically in \(c^{-2}\) as a space of states localized in the standard quantum-mechanical sense. This approach is compared with that of canonical quantization of geodesic motion of the same kind of particles in \(V_{1,3}\), carried out by the same author in [Gravit. Cosmol. 5, 23-30 (1999; Zbl 0983.83012)]. It is shown that the resulting momentum, spatial position and Hamilton operators are in general different in the two cases.