  We argue that in order to study the magneto-transport in a relativistic Weyl
fluid, it is needed to take into account the associated quantum corrections,
namely the side-jump effect, at least to second order. To this end, we impose
Lorentz invariance to a system of free Weyl fermions in the presence of the
magnetic field and find the second order correction to the energy dispersion.
By developing a scheme to compute the integrals in the phase space, we show
that the mentioned correction has non-trivial effects on the thermodynamics of
the system. Specifically, we predict the form of the negative magnetoresistance
in the system from the enthalpy density in equilibrium. Then in analogy with
Weyl semimetal, in the framework of the chiral kinetic theory and under the
relaxation time approximation, we explicitly compute the
magneto-conductivities, at low temperature limit ($T\ll \mu$). We show that the
conductivities obey the set of Ward identities which follow from the generating
functional including the Chern-Simons part.
