  As shown by Gertsenshtein in 1961, an external magnetic field can couple
electromagnetic to gravitational waves, giving rise to oscillations between
them. Viewed as a quantum process, the magnetic field has catalyzed the mixing
of photon and graviton states. We show that the self-interaction terms of the
Yang-Mills SU(2) field can take the place of the external magnetic field and
autocatalyze the mixing of Yang-Mills bosons and gravitons. In the process,
rotational symmetry is broken and the Yang-Mills boson acquires a mass.
