The purpose of this note is threefold: (i) to recall (with some points made more explicit) the mathematical Weyl algebra model formulation, given before, of the Staruszkiewicz theory of quantum Coulomb field; (ii) to add some new elements to the discussion of the representation of the Lorentz group within this model; (iii) to comment on some statements on the structure of the theory which appeared recently.

We examine the alpha and heavier cluster decay half-lives of the nuclei for 87≤Z≤96 using the analytical formula obtained by the Wentzel-Kramers-Brilliouin (WKB) method within the framework of the cluster model for the modified harmonic oscillator and spherical Coulomb potential. We correlate the clustering effect in the nuclei with the nuclear potential depth only and systematically investigate the alpha and heavier cluster decay half-lives. In addition to half-lives, the branching ratios relative to alpha decay half-lives are also calculated and results are compared with experimental data. The rms deviations of the alpha and cluster decay half-lives show a good agreement with the universal decay law (UDL), Horoi, and one single line of universal (UNIV) curve models. Utilizing the optimized cluster model parameters, we also predict the half-lives of 14C, 20O, 24,25Ne, 28,30Mg, and 32Si cluster emissions from various isotopes for guiding future experiments.