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[en] In this paper, we perform the polar analysis of the spinorial fields, starting from the regular cases and up to the singular cases: we will give for the first time the polar form of the spinorial field equations for the singular cases constituted by the flag-dipole spinor fields. Comments on the role of further spinor sub-classes containing Majorana and Weyl spinors will be sketched.
[en] In this paper, we consider the most general treatment of spinor fields, their kinematic classification and the ensuing dynamic polar reduction, for both classes of regular and singular spinors; specifying onto the singular class, we discuss features of the corresponding field equations, taking into special account the sub-classes of Weyl and Majorana spinors; for the latter case, we study the condition of charge-conjugation, presenting a detailed introduction to a newly-defined type of spinor, that is the so-called ELKO spinor: at the end of our investigation, we will assess how all elements will concur to lay the bases for a simple proposal of neutrino mass generation.
[en] I systematically consider, in the context of the type-I see-saw mechanism, all the predictive cases in which both the Dirac mass matrix connecting the left-handed neutrinos to the right-handed neutrinos, and the Majorana mass matrix of the latter neutrinos, feature texture zeros, while the mass matrix of the charged leptons is diagonal. I find a few cases which had not been discussed in the literature previously. (paper)
[en] THe geometry of the Enneper-Weierstrass representation and of the Gauss map of minimal surfaces in R4 is analysed in terms of holomorphic spinor fields. The restriction to Majorana spinors and some representation of strings in R3,1 is studied. The analogy of the corresponding Gauss map with Fermi-Yang weak currents (both neutral and charged) is underlined. The geometry of Lorentzian surfaces in R2,2 is analysed in all generalities and details
[en] We give a geometric approach in the general problems of quantization, using essentially fields of spinors (symplectic or orthogonal spinors) over curved spaces (time-space). Klein-Gordon condition, Einstein equations ... etc ... mean that some linear operator is antihermitian. Our approach is convenient for usual fields (including gravitational and Yang-Mills fields) in wavy formalism. Finally we briefly indicate a corpusculary formalism
[fr]Une approche geometrique est donnee dans les problemes generaux de la quantification en utilisant des champs de spineurs (spineurs symplectiques ou orthogonaux) sur des espaces courbes (espace-temps). Condition de Klein-Gordon, equations d'Einstein ... etc ... signifient que l'operateur lineaire est antihermitien. Cette approche est commode pour les champs usuels (incluant les champs gravitationel et de Yang Mills) dans un formalisme d'onde. Finalement on indique brievement un formalisme corpusculaire
[en] It is proved that there exists a vector representation of Dirac's spinor field and in one sense it is equivalent to biquaternion (i.e. complexified quaternion) representation. This can be considered as a generalization of Cartan's idea of triality to Dirac's spinors. In the vector representation the first-order Dirac Lagrangian is dual-equivalent to the two-order Lagrangian of topologically massive gauge field. The potential field which corresponds to the Dirac field is obtained by using master (or parent) action approach. The novel gauge field is self-dual and contains both anti-symmetric Lee and symmetric Jordan structure.
[en] We point out a limiting procedure which enables one to construct in supergravity theories non-gauge, linearized spin-3/2 fields with the aid of the supercovariantly constant spinors. We give an explicit application of the procedure for N = 2 supergravity. (orig.)
[en] Spinor fields on the conformally compactified Minkowski space (isomorphic to M-bar = (S1 x S3)/Z2) are discussed. The two inequivalent spin structures are found to correspond to a vierbein field on M making an even (normal case) or an odd (exotic case) number of 2π rotations along any isotropic line in M4. Fields on M4 obtained by the Dirac-Hepner-Mack-Salam method starting from Rsup(2,4) spinors cannot be extended to M-bar in the sense of both spin structures