  We investigate optical transitions of non-interacting electron systems
consisting of two symmetric energy bands touching each other at the Fermi
energy (e.g. graphene at half filling). Optical conductivity is obtained using
Kubo formula at zero temperature. We show that for particles whose pseudospin
direction is determined solely by the direction of their momentum, the optical
conductivity has power law frequency dependence with the exponent $(d-2)/z$
where $d$ is the dimension of the system and $z$ is the dynamical exponent.
According to our result two-dimensional systems with the above pseudospin
characteristics always exhibit frequency-independent optical conductivity.
