Chiral symmetry breaking in the pseudo-quantum electrodynamics

Abstract

In this work, we study the chiral symmetry breaking in pseudo-quantum electrodynamics in ($2+1$) dimensions, which is designed to reproduce a Coulomb potential for charged particles on a plane interacting via photons propagating in ($3+1$) space-time dimensions and would be relevant for applications to condensed-matter systems. Using an ultraviolet cutoff in the momentum integrals, we show that there is a critical dimensionless coupling ${\ensuremath{\alpha}}_{c}=\ensuremath{\pi}/4$ above which there is chiral symmetry breaking. In the case of the theory with $N$ massless fermions, we obtain a critical value of the number of fermion flavors, ${N}_{c}$, below which the chiral symmetry breaking occurs. Finally, we discuss the relevance of our results to graphene in the ultimate deep infrared regime where the Fermi velocity of the Dirac fermions approaches the velocity of light.