Local Field Theory and Isospin Invariance. III. Interactions of Self-Conjugate Isofermion Fields

Abstract

Interactions involving self-conjugate fields of arbitrary spin and half-integral isospin are studied. (The abbreviation SCIF is used for "self-conjugate isofermion.") In the absence of interactions, SCIF theories are nonlocal but relativistically covariant. In the presence of interactions, the covariance is lost because the interaction Hamiltonian density fails to commute with itself at spacelike separations. Typical interactions involving SCIF's either contain no pair (creation and destruction) terms or only pair terms. Thus, in general, crossing symmetry is lost. A model is exhibited in which the "invariant" scattering amplitude is not a Lorentz-invariant function of Lorentz scalars. In a crossed channel the scattering amplitude vanishes identically. Strong, electromagnetic, and weak interactions of SCIF's are studied with emphasis on the experimental properties of such objects. SCIF's can only interact in pairs with photons and normal hadrons because of selection rules, independently of the proportionality factor between charge $Q$ and isospin component ${I}_{3}$. A SCIF is stable under strong and electromagnetic interactions. SCIF's can be produced in pairs through strong and electromagnetic interactions, the latter only if aided by strong interactions. If the SCIF charges are half-integral, the current-current weak interaction can lead to SCIF pair production with the aid of the strong interactions, when the SCIF field contributes to the weak current. The possibility of the $W$ meson being a SCIF is investigated. Identifying ${W}^{\ifmmode\pm\else\textpm\fi{}}$ with the ${I}_{3}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$, $Q=\ifmmode\pm\else\textpm\fi{}1$ members of a SCIF isospin doublet, we have two distinct types of coupling. The charged current ${J}^{+}$ can be coupled to (${W}^{+},{W}^{+*}$) or to (${W}^{\ensuremath{-}*},{W}^{\ensuremath{-}}$) (${W}^{+*}\ensuremath{\not\equiv}{W}^{\ensuremath{-}}$ for SCIF theories). Neither $J\ifmmode\cdot\else\textperiodcentered\fi{}W$ coupling is $\mathrm{CPT}$ invariant but the effective $J\ifmmode\cdot\else\textperiodcentered\fi{}J$ coupling is $\mathrm{CP}$, $T$, and $\mathrm{CPT}$ invariant if only one of the possibilities is employed. (We specialize to the case of a $T$-invariant theory.) If instead we couple one current to (${W}^{+},{W}^{+*}$) and another to (${W}^{\ensuremath{-}*},{W}^{\ensuremath{-}}$), the effective current-current interaction involving cross terms is $\mathrm{CP}$-noninvariant. This $\mathrm{CP}$-violating interaction is noncovariant and involves an energy dependence roughly of the form $\frac{\ensuremath{\Delta}E}{{m}_{W}}$, where $\ensuremath{\Delta}E$ is the mean energy transferred by the currents.