Fermion propagator in a rotating environment

Alejandro Ayala,L A Hernández,R Zamora,K Raya

doi:10.1103/physrevd.103.076021

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.

Highlights

Collisions of heavy nuclei at high energies produce deconfined strongly interacting matter, dubbed as the quark-gluon plasma (QGP)
When the vortical motion is transferred to the particles spin within the QGP, its effect can show, upon hadronization, as a global hadron polarization, namely, a preferred direction of the spin of hadrons along the normal to the reaction plane
As we show in this work, this can be done provided we keep the first nontrivial contribution in the angular velocity Ω, which is taken as a large quantity compared to the expansion rate Γ, effectively making fermions partake of the rigid rotational motion

Summary

INTRODUCTION

Collisions of heavy nuclei at high energies produce deconfined strongly interacting matter, dubbed as the quark-gluon plasma (QGP) When these collisions are off-center, the inhomogeneity of the matter distribution in the transverse plane causes the colliding region to develop an orbital angular velocity Ω directed along the normal to the reaction plane [1,2]. As we show in this work, this can be done provided we keep the first nontrivial contribution in the angular velocity Ω, which is taken as a large quantity compared to the expansion rate Γ, effectively making fermions partake of the rigid rotational motion. Lattice QCD has been formulated in rotating frames to study the angular momenta of gluons and quarks in a rotating QCD vacuum [38] In all these calculations, the causality condition, whereby the angular velocity and the cylinder radius R must satisfy RΩ < 1, is imposed.

FERMIONS IN A RIGIDLY ROTATING CYLINDER

FERMION PROPAGATOR IN A RIGIDLY ROTATING CYLINDER

SUMMARY AND OUTLOOK