  Symmetries associated with the Hamiltonian describing bilayer graphene
subjected to a constant magnetic field perpendicular to the plane of the
bilayer are calculated using polar coordinates. These symmetries are then
applied to explain some fundamental properties, such as the spectrum and the
integer pseudo-spin character of the eigenfunctions. The probability and
current densities of the bilayer Hamiltonian have also been calculated in polar
coordinates and shown to be gauge invariant and scalar under generalized
rotations. We also define appropriate coherent states of this system as
eigenfunctions, with complex eigenvalues, of a suitable chose annihilation
operator. In this framework, symmetries are also useful to show the meaning of
the complex eigenvalue in terms of expected values. The local current density
of these coherent states is shown to exhibit a kind of radial component
interference effect, something that has gone unnoticed until now. Some of these
results that have just been exposed are graphically illustrated throughout the
manuscript.
