A NEW THEOREM ON THE REPRESENTATION STRUCTURE OF THE SL (2, C) GROUP ACTING IN THE HILBERT SPACE OF THE QUANTUM COULOMB FIELD

Using the results obtained by Staruszkiewicz in Acta Phys. Pol. B 23, 591 (1992) and in Acta Phys. Pol. B 23, 927 (1992), we show that the representations acting in the eigenspaces of the total charge operator corresponding to the eigenvalues n(1); n(2) whose absolute values are less than or equal root pi/e(2) are inequivalent if vertical bar n(1)vertical bar not equal vertical bar n(2)vertical bar and contain the supplementary series component acting as a discrete component. On the other hand, the representations acting in the eigenspaces corresponding to eigenvalues whose absolute values are greater than root pi/e(2) are all unitarily equivalent and do not contain any supplementary series component.