Quantum mechanics in Riemannian space-times. I: Canonical approach (Q1576104)

The canonical quantization of geodesic motion of a neutral spinless point-like particle in the general Riemannian space-time \(V_{1,3}\) is studied, using the \(1+3\)-foliation of space-time by normal geodesic translation of an arbitrary but fixed Cauchy hypersurface. It is shown that the resulting structure is similar to the Schrödinger picture of the standard non-relativistic quantum mechanics with the Born probabilistic interpretation of the wave functions. A possible physical interpretation of the state vectors and the position operators is discussed. For Part II, see ibid. 5, No. 1, 31-39 (1999; Zbl 0983.83013) below.