  The computation of the optical conductivity of strained and deformed graphene
is discussed within the framework of quantum field theory in curved spaces. The
analytical solutions of the Dirac equation in an arbitrary static background
geometry for one dimensional periodic deformations are computed, together with
the corresponding Dirac propagator. Analytical expressions are given for the
optical conductivity of strained and deformed graphene associated with both
intra and interbrand transitions. The special case of small deformations is
discussed and the result compared to the prediction of the tight-binding model.
