Conformal invariance of massless Duffin–Kemmer–Petiau theory in Riemannian spacetimes

Abstract

We investigate the conformal invariance of massless Duffin–Kemmer–Petiau theory coupled to Riemannian spacetimes. We show that, as usual, in the minimal coupling procedure only the spin 1 sector of the theory—which corresponds to the electromagnetic field—is conformally invariant. We also show that the conformal invariance of the spin 0 sector can be naturally achieved by introducing a compensating term in the Lagrangian. Such a procedure—besides not modifying the spin 1 sector—leads to the well-known conformal coupling between the scalar curvature and the massless Klein–Gordon–Fock field. Going beyond the Riemannian spacetimes, we briefly discuss the effects of a nonvanishing torsion in the scalar case.