Wave function of the photon in a curved spacetime

Abstract

It is known that the classical variables are replaced by operators for the dynamics of the electromagnetic field, thus the second quantization is traditionally used. There is a significant question in modern theoretical physics area: “Why is there no fully developed first-quantized theory of photons?” In the present work, we argue that a photon wave function can be obtained if one uses the massless Duffin-Kemmer-Petiau (mDKP) equation. Thus, we focus on exact solutions of the mDKP equation the Robertson–Walker type spacetime via the Teleparallel Theory (TPT) of Gravity. The mDKP equation is generally known as the spinor formulation of the photons. We also focus on solutions of the Maxwell equations (MEs) to verify the equivalence between the mDKP and the ME formulations of the photons. It is shown that photons present an oscillatory behavior.