  Recently, negative longitudinal and positive in-plane transverse
magnetoresistance have been observed in most topological Dirac/Weyl semimetals,
and some other topological materials. Here we present a quantum theory of
intrinsic magnetoresistance for three-dimensional Dirac fermions at a finite
and uniform magnetic field B. In a semiclassical regime, it is shown that the
longitudinal magnetoresistance is negative and quadratic of a weak field B
while the in-plane transverse magnetoresistance is positive and quadratic of B.
The relative magnetoresistance is inversely quartic of the Fermi wave vector
and only determined by the density of charge carriers, irrelevant to the
external scatterings in the weak scattering limit. This intrinsic anisotropic
magnetoresistance is measurable in systems with lower carrier density and high
mobility. In the quantum oscillation regime a formula for the phase shift in
Shubnikov-de Hass oscillation is present as a function of the mobility and the
magnetic field, which is useful for experimental data analysis.
