We study the quantum Hall effect in graphene at filling factors \nu = 0 and
\nu = \pm, concentrating on the quantum Hall ferromagnetic regime, within a
non-perturbative bosonization formalism. We start by developing a bosonization
scheme for electrons with two discrete degrees of freedom (spin-1/2 and
pseudospin-1/2) restricted to the lowest Landau level. Three distinct phases
are considered, namely the so-called spin-pseudospin, spin, and pseudospin
phases. The first corresponds to a quarter-filled (\nu =-1) while the others to
a half-filled (\nu = 0) lowest Landau level. In each case, we show that the
elementary neutral excitations can be treated approximately as a set of
n-independent kinds of boson excitations. The boson representation of the
projected electron density, the spin, pseudospin, and mixed spin-pseudospin
density operators are derived. We then apply the developed formalism to the
effective continuous model, which includes SU(4) symmetry breaking terms,
recently proposed by Alicea and Fisher. For each quantum Hall state, an
effective interacting boson model is derived and the dispersion relations of
the elementary excitations are analytically calculated. We propose that the
charged excitations (quantum Hall skyrmions) can be described as a coherent
state of bosons. We calculate the semiclassical limit of the boson model
derived from the SU(4) invariant part of the original fermionic Hamiltonian and
show that it agrees with the results of Arovas and co-workers for SU(N) quantum
Hall skyrmions. We briefly discuss the influence of the SU(4) symmetry breaking
terms in the skyrmion energy.Comment: 16 pages, 4 figures, final version, extended discussion about the
boson-boson interaction and its relation with quantum Hall skyrmion
