Part I.
A π-meson decays into µ-meson and neutrino at least 1000 times faster thaninto an electron and a neutrino. After summarizing the difficulties inassuming that electrons or µ-mesons interact with nucleons through theintermediary of the π-meson, the decay of the π is discussed for the symmetriccoupling scheme in which electrons and µ-mesons interact directly withnucleons. Selection rules rigorously forbid this decay for the most choices ofthe π-meson field and the form of nuclear β-decay. For the very specialcase of pseudoscalar meson and pseudovector β-decay (with arbitrary mixturesof scalar, vector and tensor) the decay rate for π → (µ,v) proceeds 104times as fast as π → (µ,v) and 10+3 as fast as π → (photon, e, v).This result is independent of perturbation theory. Agreement with theobserved lifetime can be obtained if the divergent integral is cut off at the nucleon Compton wavelength.
Part II.
A unitary theory of particles is investigated, mostly on the classical level.The Dirac and the Klein-Gordon equations are augmentedby simple non-linear terms. Interpreted as wave equations forclassical fields they contain a much richer variety of solutions thanthe customary linear theories. Particles, instead of having independent existences as singularities, appear only as intense localized regions ofstrong field. Solutions of the field equations are subject to theboundary condition that the fields be regular everywhere and that allobservable integrals be finite. For simple angular and temporaldependence the wave equation reduces to a set of ordinary differentialequations. The boundary condition leads to a non-linear eigenvalueproblem whose solutions are systematically described in the phase plane.Numerical solutions are found for some typical cases. The masses of theparticles are positive; the number carrying unit charge is small. Thescalar field variables can be interpreted in terms of operators according tothe usual commutation rules, but the particles are unstable when perturbedby quantum fluctuations. The application of anti-commutation rules to the spinor fields has no classical limit. The lack of satisfactory recipe forquantizing classical spinor fields makes the interpretation of the particle-likesolutions obscure.
