| Abstract: | In coupling gravity with the quantum field theory, unitary transformations, depending on space-time-points, were considered and derivatives were introduced, which imply a nonintegrable parallel transport of the state vectors of Hilbert space 1]. The Dirac equation, built with these generalized derivatives, is quantized in a prescribed classical gravitational field. The quantization can be performed in complete analogy to the usual procedure in Minkowski space, but the quantum state vector becomes path dependent. In carrying out the quantization, two two-component classical spinor fields necessarily occur, which obey Weyl's equation. The considered quantized Dirac equations are also picture-covariant, that is they have the same from in each physical picture, especially in the Heisenberg picture and the Schrödinger picture. |
