  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.
