  It is well-known that the tight-binding Hamiltonian of graphene describes the
low-energy excitations that appear to be massless chiral Dirac fermions. Thus,
in the continuum limit one can analyze the crystal properties using the
formalism of quantum electrodynamics in 2+1 dimensions (QED2+1) which provides
the opportunity to verify the high energy physics phenomena in the condensed
matter system. We study the symmetry properties of 2+1-dimensional Dirac
equation, both in the non-interacting case and in the case with constant
uniform magnetic field included in the model. The maximal symmetry group of the
massless Dirac equation is considered by putting it in the Jordan block form
and determining the algebra of operators leaving invariant the subspace of
solutions. It is shown that the resulting symmetry operators expressed in terms
of Dirac matrices cannot be described exclusively in terms of gamma matrices
(and their products) entering the corresponding Dirac equation. It is a
consequence of the reducibility of the considered representation in contrast to
the 3+1-dimensional case. Symmetry algebra is demonstrated to be a direct sum
of two gl(2,C) algebras plus an eight-dimensional abelian ideal. Since the
matrix structure which determines the rotational symmetry has all required
properties of the spin algebra, the pseudospin related to the sublattices (M.
Mecklenburg and B. C. Regan, Phys. Rev. Lett. 106, 116803 (2011)) gains the
character of the real angular momentum, although the degrees of freedom
connected with the electron's spin are not included in the model. This seems to
be graphene's analogue of the phenomenon called "spin from isospin" in high
energy physics.
