On the problem of constraints in minimally coupled relativistic wave equations for particles of unique mass

Abstract

We study the problem of a possible change in the number of constraints in linear relativistic wave equations (-iβ_μ ∂^μ +m)φ=0 for particles of unique mass, on introduction of minimal coupling to an external electromagnetic field. Complementing our earlier work in which we obtained conditions for non-loss of constraints in equations characterised by the minimal β-algebra β₀⁵=β₀³ we derive here the conditions for such theories not to generate more constraints than in the free case. The results are illustrated by considering specific equations and a fallacy in certain conclusions of Kobayashi and Shamaly on this problem is pointed out.