On the In teractions of Mesons with the Electromagnetic Field

Abstract

By means of the formalism of Duffin and Kemmer there is constructed for mesons interacting with the electromagnetic field a theory that is manifestly Lorentz invariant and also gauge invariant and invariant under charge conjugation. The transformation to an interaction representation is accomplished by a procedure necessarily somewhat more complicated than that used by Schwinger for the quantum electrodynamics of electrons. The longitudinal components of the electromagnetic field are eliminated in a covariant manner.The resulting interaction Hamiltonian is analyzed into terms corresponding to self-energies and terms describing interactions. By a suitable interpretation of ambiguous expressions, the photon self-energy is shown to vanish. Expressions are found for the polarization of the mesic vacuum by a given electromagnetic field. In the case of mesons of spin 1, not only the term proportional to the original current, but also that proportional to its d'Alembertian has an infinite factor. A formal procedure for the unambiguous exclusion of such infinite contributions is suggested. Explicit expressions are found for the self-energies of scalar and vector mesons. These self-energies can be eliminated by renormalization of mass.