Fermion propagator in a rotating environment

Abstract

We apply the exponential operator method to derive the propagator for a fermion immersed within a rigidly rotating environment with cylindrical geometry. Given that the rotation axis provides a preferred direction, Lorentz symmetry is lost and the general solution is not translationally invariant in the radial coordinate. However, under the approximation that the fermion is completely dragged by the vortical motion, valid for large angular velocities, translation invariance is recovered. The propagator can then be written in momentum space. The result is suited to be used applying ordinary Feynman rules for perturbative calculations in momentum space.

Position-space representation of charged particles’ propagators in a constant magnetic field as an expansion over Landau levels

“…However, for particles with spin, it significantly simplifies the notation and provides additional representations of the propagator. It should also be noted that the effectiveness of the MFS method was demonstrated in a different physical scenario, namely, the method was applied by other authors to calculate the fermion propagator in a rotating environment [38]. We also believe that this approach could appear to be useful for the calculations of particle propagators in various physical environments.…”

“…We observe that, aside from the overall non-invariant phase factor e iΦ , the summation terms in (38) decompose into two factors. The first one depends only on the x, y-coordinates and is invariant with respect to rotations in the x, y-plane which is perpendicular to the direction of the magnetic field.…”