  Starting from the Luttinger model for the band structure of GaAs, we derive
an effective theory that describes the coupling of the fractional quantum Hall
(FQH) system with photons in resonant Raman scattering experiments. Our theory
is applicable in the regime when the energy of the photons $\omega_0$ is close
to the energy gap $E_G$, but $|\omega_0-E_G|$ is much larger than the energy
scales of the quantum Hall problem. In the literature, it is often assumed that
Raman scattering measures the dynamic structure factor $S(\omega,\mathbf{k})$
of the FQH. However, in this paper, we find that the light scattering spectrum
measured in the experiments are proportional to the spectral densities of a
pair of operators which we identified with the spin-2 components of the kinetic
part of the stress tensor. In contrast with the dynamic structure factor, these
spectral densities do not vanish in the long-wavelength limit $k\to0$. We show
that Raman scattering with circularly polarized light can measure the spin of
the magnetoroton excitation in the FQH system. We give an explicit expression
for the kinetic stress tensor that works on any Landau level and which can be
used for numerical calculations of the spectral densities that enter the Raman
scattering amplitudes. We propose that Raman scattering provides a way to probe
the bulk of the $\nu=5/2$ quantum Hall state to determine its nature.
