  The influence od space-time curvature on quantum matter which can be
theoretically described by covariant wave equations has not been experimentally
established yet. In this paper we analyse in detail the suitability of the
Ramsey atom beam interferometer for the measurement of the phase shift caused
by the Riemannian curvature of the earth. It appears that the detection should
be possible with minor modifications of existing devices within the near
future. The paper is divided into two parts. The first one is concerned with
the derivation of general relativistic correction terms to the Pauli equation
starting from the fully covariant Dirac equation and their physical
interpretation. The inertial effects of acceleration and rotation are included.
In the second part we calculate the phase shift as seen in a laboratory resting
on the rotating earth and examine various possibilities to enlarge the
sensitivity of the apparatus to space-time curvature. Some remarks on the
Lense-Thirring effect and on gravitational waves are made. Since the two parts
may be more or less interesting for physicists with different research fields
they are written in such a way that each one may be read without much reference
to the other one.
