ISSN 1330–0016 CODEN FIZBE7 SIGNIFICANCE OF THE SPINORIAL BASIS IN RELATIVISTIC QUANTUM MECHANICS VALERI V. DVOEGLAZOV 1 Escuela de F´ ısica, Universidad Aut´ onoma de Zacatecas Antonio Doval´ ı Jaime s/n, Zacatecas 98068, ZAC., M´ exico Internet address: VALERI@CANTERA.REDUAZ.MX Received 7 March 1997 UDC 539.183.4 PACS numbers: 03.65.Pm, 11.30.Er The problems related to the choice of the spinorial basis in the j 0 0 j representation space are discussed. This choice is shown to have a profound significance in the relativistic quantum theory and for physical applications. From the methodological viewpoint, this fact is related to the important dynamical role which the space-time symmetries play for all kinds of interactions. 1. Introduction We have become accustomed to thinking of the particle world from a viewpoint of the principle of gauge invariance. Profound significance of this principle seems to be clear to everybody and it deserves to be in the place that it occupies now. Remarkable experi- mental confirmations of both quantum electrodynamics [1] and its non-Abelian extensions (Weinberg-Salam-Glashow model, quantum chromodynamics), Refs. 2 and 3, proved the applicability of this principle. As is known, the principle has primarily been deduced from the interaction of charged particles with the electromagnetic potential. For long, it has 1 On leave of absence from Dept. Theor. & Nucl. Phys., Saratov State University, Astrakhanskaya ul., 83, Saratov RUSSIA. Internet Address: dvoeglazov@main1.jinr.dubna.su FIZIKA B 6 (1997) 3, 111–122 111