The formulation of the generally covariant analog of standard (nonrelativistic) quantum
mechanics in a general Riemannian spacetime begun in earlier studies of the author is …

A general covariant analog of standard nonrelativistic quantum mechanics with relativistic
corrections is constructed for the Dirac particle in a normal geodesic frame in general …

Expressions for the operators of momentum and kinetic energy in the Riemannian space are
obtained from general quantummechanical requirements. The results make it possible to …

Quantum Mechanics and Quantum Field Theories in the Quantized Space. II Quantum
Mechanics Page 1 883 Progress of Theoretical Physics, Vol. 113, No. 4, April 2005 Quantum …

5. Discussion In this paper, we have proposed a quantum theory of a relativistic string in
fourdimensional space. Note that the gauge conditions (12) and (21), which played a key …

Covariant four-vector position operators X μ are proposed, which form a natural operator
generalization of the four-position in relativistic classical mechanics. These X μ are defined …

The Riemannian phase space theory is developed here. It is a generalization of the usual
Lorentz invariant theory. Its basic formulation is given in order to apply quantum physics, ie …

Basic properties of the quantum spinor field theory in the Riemannian space-time are
described. Both real and complex fields are considered. 5 refs.(author).

Non-relativistic quantum mechanics is formulated here in a different way. It is, however,
mathematically equivalent to the familiar formulation. In quantum mechanics the probability …

Yo=(A2+ y2) 1! 2l, 1.> 0, and S is any space-or-lightlike submanifold of space-time R n+'.
The CT'S have natural symplectic structures covariant with respect to the Poincare group …