▎ 摘　　要

Quantization of the gauge models is significant in theoretical physics. Graphene is magical material of the 21th century, so in this search we have employed the BFT approach to study dynamic of an electron on the Dirac points of graphene. Here we considered the graphene as a constrained system in non-commutative space with second class constraints so its gauge symmetries are broken. In the approach first the phase space is extended then the constraint series and Hamiltonian are rewritten such that the 2 (nd) class constraints are converted to the 1 (st) ones. As result, we introduce a gauge symmetry for moving an electron on the Dirac points of graphene and calculate its partition function.