Narrow Results

It is shown that on the de Sitter spacetime the global behavior of the free Dirac spinors in momentum representation is determined by several phase factors which are functions of momentum with special properties. Such suitable phase functions can be chosen for writing down the free Dirac quantum modes of the spin basis that are well-defined even for the particles at rest in the moving local charts where the modes of the helicity basis remain undefined. Under quantization, these modes lead to a basis in which the one-particle operators keep their usual forms apart from the energy operator which lays out a specific term depending on the concrete phase function one uses.

We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations, the operator contains the scalar curvature as a multiplicative term. We show that such term can be cancelled or added with an arbitrary constant factor, both in the mainstream geometric quantization and in the covariant quantum mechanics developed by Jadczyk and Modugno with several contributions from many authors.