  Cross sections for photon production in hadronic scattering processes have
been calculated according to an effective chiral field theory. For $\pi + \rho
\to \pi + \gamma$ and $\pi + \pi \to \rho + \gamma$ processes, these cross
sections have been implemented into a novel hadronic transport approach
(SMASH), which is suitable for collisions at low and intermediate energies. The
implementation is verified by systematically comparing the thermal photon rate
to theoretical expectations. The photon rates we obtain are compared to
previous works, where scattering processes mediated by $\omega$ mesons are
found to contribute significantly to the total photon production. Finally, the
impact of considering the finite width of the $\rho$ meson is investigated, and
a significant enhancement of photon production in the low-energy region is
observed. This work is the first step towards a consistent treatment of photon
emission in hybrid hydrodynamics+transport approaches. The quantification of
the importance of the hadronic stage for the resolution of the direct photon
flow puzzle is a next step and can be applied to identify equilibrium and
non-equilibrium effects in the hadronic afterburner.
