Radiance fields have no concept of light emission, reflection, absorption, etc. instead everything is mushed into one value: The light transported. In that sense radiance fields are just 3D photos.
You would have to perform reverse-rendering / photo grammetry and estimate where the light sources and the surfaces are, what materials they have and so on. Then you could use traditional path tracing methods on that again.
Another thing to think about might be videos (not animation): Continuously capture the radiance field over time and then try to compress away the similarities in between frames to gain temporal coherence.