Helical massive fermions under rotation

Abstract

The properties of a massive fermion field undergoing rigid rotation at finite temperature and chemical potential are discussed. The polarisation imbalance is taken into account by considering a helicity chemical potential, which is dual to the helicity charge operator. The advantage of the proposed approach is that, as opposed to the axial current, the helicity charge current remains conserved at finite mass. A computation of thermal expectation values of the vector, helicity and axial charge currents, as well as of the fermion condensate and stress-energy tensor is provided. In all cases, analytic constitutive equations are derived for the non-equilibrium transport terms, as well as for the quantum corrections to the equilibrium terms (which are derived using an effective relativistic kinetic theory model for fermions with helicity imbalance) in the limit of small masses. In the context of the parameters which are relevant to relativistic heavy ion collisions, the expressions derived in the massless limit are shown to remain valid for masses up to the thermal energy, except for the axial charge conductivity in the azimuthal direction, which presents strong variations with the particle mass.

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

“…[81], while the mass term agrees with the correction found in Equations (7.10) and ( 40) of Refs. [61,82], respectively, as well as with the high temperature expansion of the results derived in Ref. [83] (see last entry for W A in Table 2).…”

“…The above expressions are identical to the vanishing chemical potential limit (µ V = µ H = 0) of Equation (4.22) in Ref. [61]. The large temperature limit can be computed using Equation (A18) to expand the modified Bessel functions:…”

“…where the hat over the integration measure was added to indicate that the integration is performed with respect to the tetrad components of the momentum vector. Contracting Equation (37) with η α β and u αu β, the energy density and pressure can be shown to satisfy [61]:…”

“…where C is the Euler-Mascheroni constant (A13). Substituting the above into Equation (41) and using Equation (A4) to perform the summation over j, we can derive the following expansions [61]:…”

“…According to the analysis on Minkowski space [21,61,79], the t.e.v. of the SC for small masses M = k −1 is given by…”