theory of their

Dirac equation in (1+2) dimensions for quasi-particles in graphene and quantum field theory of their Coulomb interaction. Abstract There is evidence for existance of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's bril-luoin zone. Certain subtle points which are peculiar to odd number of space-time dimensions (in this case three), in the derivation of such an equation are clarified. It is shown that parity operator in (1+2) dimensions play an intersting role and can be used for defining conserved chiral currents [there is no γ 5 in (1+2) dimensions] resulting from the underlying Lagrangian for massless Dirac quasi-particles in graphene which is shown to have chiral U L (2) × U R (2) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self energy and the renormalization of the effective coupling of this interaction and Fermi velocity. Recently there has been a lot of interest in graphene. On experimental side it has some anomalous magnetic and transport properties[1]. On theoretical side its low energy excitations are massless, chiral Dirac fermions[1]. This implies existence of quasi-particles in graphene, which satisfy massless Dirac equation in (1+2) dimensions near the so called Dirac points which 1