Die Stromdichte eines quadratisch integrierbaren Klein-Gordon-Feldes mit Wechselwirkung

A four vector is constructed for the statistical interpretation of a relativistic scalar wave function which is not a solution of an interaction-free Klein-Gordon equation. The zero component of the four vector is positive definite, whereas the four components satisfy the equation of continuity. It is proved that these components, which are bilinear forms inΨ(x)=∫d ⁴pa(p)e^?ipxsatisfying the normalization condition(2π) ⁴(2m)^?1∫ d⁴pθ(p⁰)θ6(p²)¦a(p)¦²=1 reduce to the four-vector ofPetzold and co-workers if the transition fromΨ(x) to the free-particle wave functionΦ(x)=∫d ³¯pa(¯p)e^?ipxsatisfying(2π) ³ (2m)^?1∫(2p₀)^?1¦a (¯p)¦²d³¯p=1 is made in the proper way. The nonrelativistic limit in the case of relativistic interactions is also discussed.