Abstract
Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrated that the three-dimensional chiral transport equations are consistent with the chiral anomaly. For massive fermions the three-dimensional kinetic transport theory generated by the new covariant kinetic equations is established in small mass limit. It possesses the Coriolis force and the massless limit can be obtained directly.
Highlights
Yields some different covariant kinetic equations [18, 19], in contrary to the massless case
We present the underlying action and show that the resulting equations of motion are identical to the Euler equations in the presence of Coriolis force
This is due to the fact that for massive fermions there are more than one way of eliminating the irrelevant set of field equations derived from the quantum kinetic equation (QKE)
Summary
We are interested in expressing the vector field ηα in terms of fluid variables like the enthalpy current. In relativistic fluid dynamics particle number current density without dissipation is given with (3.9) [32] Equipped with these relations we may discuss why we consider the action (2.1). (3.6) represents this interaction because the variation of the action (2.1) with respect to Aμ shows that (3.7) is the current which describes how the electromagnetic fields will evolve in plasma:. By inspecting (3.11) we see that interaction of the fluid with electromagnetic fields is exposed by setting ηα This shows that scalar field components couple to the derivatives of the electromagnetic fields which would be calculated from the Maxwell equations (3.14) whose charge and current distributions are due to the charged fermions. The field strength of ηα is given by (3.46) when the equations of motion resulting from the variation of SF with respect to φ and ηα are satisfied
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