Kinematics ofKl3Decay Amplitudes and Relativistic Equations for Spin-0 Particles

The standard $S$-matrix kinematic analysis is applied to the $K_{l3\mathrm{}}$ decays to show that the form factors $f_{\pm }\mathrm{}\left(t\right)\mathrm{}$ are free of kinematic singularities or constraints. The general form of the matrix elements of the vector current and its divergence in the Duffin-Kemmer formalism are determined and shown to be consistent with the general kinematic analysis, in contrast to a form proposed in some recent letters.