Infinite-Component Wave Equations in the External Electromagnetic Field

Abstract

The properties of a large class of infinite-component relativistic wave equations are investigated after the inclusion of the external electromagnetic fields. The external electromagnetic fields are introduced by applying the familiar prescription $p\ensuremath{\rightarrow}p\ensuremath{-}eA$, which guarantees gauge invariance. In the expression for the energy of the particle in the external field, we first recognize terms which are familiar from the formalism of the Dirac particle in the external field, and then note the presence of new terms which are characteristic of the composite structure. The well-known $\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ term, which describes the interaction of particle spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}$ with the external magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$, appears multiplied by a constant too small to account for the experimental value of the magnetic moment of the proton. In some models, this constant can also be negative or can vanish. The results go beyond reconfirming early suspicions that, unlike the situation with the Dirac electron, the electromagnetic properties of composite particles described by the infinite-component wave equations cannot be accounted for exclusively by the prescription $p\ensuremath{\rightarrow}p\ensuremath{-}eA$. The magnetic moment associated to the procedure $p\ensuremath{\rightarrow}p\ensuremath{-}eA$ is established as a highly model-dependent physical quantity, and the mechanism which is responsible for the large variations in its value is identified. The unreasonable physical predictions concerning the magnetic moment can always be remedied through the addition of the phenomenological Pauli interaction term ${L}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$, multiplied by an appropriate real constant.