caa a22 4500 469035722 CHVBK 20180323132755.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01036532 doi (NATIONALLICENCE)springer-10.1007/BF01036532 Dirac equation and spin 1 representations, a connection with symmetries of the Maxwell equations [Elektronische Daten] [I. Krivskii, V. Simulik] A unitary operator on the space of spinors that makes it possible to associate each transformation in this space with a transformation in the space of electromagnetic field strengths is found. A connection is established by means of this operator between representations in the space of spinors and the space of field strengths for the Lorentsz, Poincaré, and conformal groups. Unusual symmetries of the Dirac equation are found on this basis. It is noted that the Pauli—Gürsey symmetry operators (without the γ5 operator) of the Dirac equation withm=0 form the same representation D(1/2, 0)⊕D(0, 1/2) of the O(1, 3) algebra of the Lorentz group as the spin matrices of the standard spinor representation. It is shown that besides the standard (spinor) representation of the Poincaré group, the massless Dirac equation is invariant with respect to two other representations of this group, namely, the vector and tensor representations specified by the generators of the representations D(1/2, 1/2) and D(1, 0) ⊕D(0, 0) of the Lorentz group, respectively. Unusual families of representations of the conformal algebra associated with these representations of the group O(1, 3) are investigated. Analogous O(1, 2) and P(1, 2) invariance algebras are established for the Dirac equation withm>0. Plenum Publishing Corporation, 1992 Krivskii I. aut Simulik V. aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 90/3(1992-03-01), 265-276 0040-5779 90:3<265 1992 90 11232 https://doi.org/10.1007/BF01036532 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01036532 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Krivskii I. aut NATIONALLICENCE 700 1- Simulik V. aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 90/3(1992-03-01), 265-276 0040-5779 90:3<265 1992 90 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer