Note on the correspondence between the classical and quantum theories of neutral mesons

Abstract

The classical theory of mesons only contains the fundamental constant ξ. The rest mass μ of the meson is introduced only when the theory is quantized by the relation μ=χ. As a result, although the quantum theory goes over strictly into the classical theory when → 0, the classical theory corresponds not only to the limit in which the momentum properties of mesons can be neglected, but also to the limit μ=0 (but ξ a finite constant). Due however to the fortunate circumstance that in nature M»μ (M being the neutron mass) the classical theory can be used extensively to calculate processes involving mesons and heavy particles, but is entirely inadequate for calculating processes involving mesons and electrons or neutrinos, just because here μ»m (m being the electron mass).