Holonomy in the Schwarzschild-Droste geometry (Q2724839)

The investigation of parallel transport of vectors and spinors in the Schwarzschild geometry is made. It is shown that the results of this investigation can be linked to some interesting phenomena. One important example of possible relevance of this study is the Einstein-Podolsky-Rosen gedanken experiment. If the participating particles move in a region of non-negligible gravitational field, the standard approach to the Einstein-Podolsky-Rosen paradox must be radically reformulated. It is also worth pointing out that in the holonomy band structure discussed in this paper there is an example of quantization that does not depend on Planck's constant. The similarity between the holonomy map and the expression for the phase that appears in quantum mechanical path integration is discussed.