  We develop an effective surface theory for the surface states of a Weyl
semimetal. This theory includes the peculiar Fermi arc states on the surface as
well as leakage of the states from the surface to the bulk. Subjecting the
model to a magnetic field perpendicular to the surface results in quantum
oscillations. The oscillations are different from the usual ones since they do
not involve a closed Fermi surface cross section. It has been shown previously
that the Quantum oscillations can be understood semiclassically as resulting
from motion of electrons on the surface Fermi arcs as well as tunneling through
chiral Landau levels associated with the bulk. In this work we develop an
effective surface theory and use it to analyze the quantum oscillation in the
semiclassical regime and beyond. Specifically, we show that when a pair of Weyl
points are close to each other the surface quantum oscillations acquire a phase
offset which originates from the bulk. While the surface states are responsible
for a large part of the electron motion, tunneling through the bulk is
necessary for completing the orbit. This tunneling makes use of the bulk, zero
energy, chiral Landau level in each Weyl node. When the nodes are close in
momentum space their chiral levels overlap and a gap at zero energy is formed.
This gap causes the phase offset in the surface quantum oscillations.
