The thermal Green's function method has been used to calculate the rea
l part of the optical conductivity in the gauge-held model. The gauge
invariant response functions were considered to the second order of th
e gauge field. We found that there is a structure in the frequency ran
ge of a fraction of the Fermi energy. It is due to the excitation of p
article-hole pair and a gauge field by a photon. In the small-frequenc
y region, the optical conductivity is sensitive to temperature because
of boson excitations. In the intermediate and high frequency region i
t is not sensitive because fermion excitations dominates.