  Chirality or handedness in condensed matter induces anomalous optical
responses such as natural optical activity, rotation of the plane of light
polarization, as a result of breaking of spatial-inversion symmetry. In this
study, optical properties of a Weyl spin-orbit system with quadratic
dispersion, a typical chiral system invariant under time-reversal, are
investigated theoretically by deriving an effective Hamiltonian based on an
imaginary-time path-integral formalism. We show that the effective Hamiltonian
can be indeed written in terms of an optical chirality order parameter
suggested by Lipkin. The natural optical activity is discussed based on the
Hamiltonian.
