  As part of an ongoing series of deep GMRT surveys we have observed the
Spitzer extragalactic First Look Survey field, producing the deepest wide-field
610-MHz survey published to date. We reach an rms noise of 30 microJy/beam
before primary beam correction, with a resolution of ~6 arcsec over an area of
~4 square degrees. By combining these observations with the existing 1.4-GHz
VLA survey produced by Condon et al. (2003), along with infrared data in up to
seven wavebands from the Spitzer Space Telescope, optical photometry from SDSS
and a range of spectroscopic redshift surveys, we are able to study the
relationship between radio luminosity and star formation rate in star-forming
galaxies up to z ~ 1. The large amount of multi-wavelength data available
allows accurate k-corrections to be performed in the radio due to the knowledge
of the radio spectral index, and in the infrared through the use of a
semi-empirical radiative transfer model which models star-forming regions, warm
dust surrounding these regions, and diffuse interstellar dust, taking into
account the star formation rate, star formation history and hydrogen column
density within each galaxy. A strong correlation is seen between radio
luminosity and infrared-derived star formation rates, which is best fit by a
slightly non-linear power-law. We look for cosmic evolution in the comparative
radio brightness of star-forming galaxies by searching for deviations away from
the global relationship. Any such deviation would indicate a systematic
variation in one or more of the properties controlling synchrotron radiation,
in particular an increase in the magnetic field strengths of star-forming
galaxies. The data shows no evidence for such an effect, suggesting that there
has been little evolution in the magnetic fields of galaxies since z ~ 1.
