Conformal invariance of massless Duffin-Kemmer-Petiau theory in Riemannian space-times

TL;DR

This paper studies the conformal invariance properties of massless Duffin-Kemmer-Petiau theory in Riemannian space-times, highlighting the invariance of the electromagnetic sector and proposing a method to achieve invariance in the scalar sector.

Contribution

It demonstrates how to achieve conformal invariance in the scalar sector of the Duffin-Kemmer-Petiau theory by introducing a compensating term, extending understanding beyond the electromagnetic sector.

Findings

Spin 1 sector (electromagnetic field) is conformally invariant.

Scalar sector's conformal invariance is achieved via a compensating term.

Brief discussion on effects of torsion in non-Riemannian spacetimes.

Abstract

We investigate the conformal invariance of massless Duffin-Kemmer-Petiau theory coupled to riemannian space-times. 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 show also 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.