Quantum Features of Non-Symmetric Geometries

Abstract

Paths in an appropriate geometry are usuallyused as trajectories of test particles in geometrictheories of gravity. It is shown that non-symmetricgeometries possess some interesting quantum features. Without carrying out any quantization schemes,paths in such geometries are naturally quantized. Twodifferent non-symmetric geometries are examined forthese features. It is proved that, whatever thenon-symmetric geometry is, we always get the same quantumfeatures. It is shown that these features appear only inthe pure torsion term (the anti-symmetric part of theaffine connection) of the path equations. The vanishing of the torsion leads to the disappearance ofthese features, regardless of the symmetric part of theconnection. It is suggested that, in order to beconsistent with the results of experiments andobservations, torsion term in path equations should beparametrized using an appropriate parameter.