Spinor Fields In Spacetime Research Articles

Charge–mass sum rules for unified spinor fields in extradimensions and the prediction for the existence of tachyon quarks and tachyon leptons

Within the framework of the mechanism proposed in our previous works [Duc and Giao, J. Mod. Phys. 5, 477 (2014); Duc et al., Int. J. Theor. Phys. 54, 1071 (2015); Duc and Giao, Int. J. Theor. Phys. 55, 959 (2016)] for mass and charge creation, we consider the charge and mass spectrum of spinor fields in extradimensions. It is shown that a single spinor field in spacetime with extradimensions corresponds to a set of effective spinor fields in ordinary four-dimensional spacetime with charges and masses obeying the sum rules dictated from some specific assumptions related to the compactification of extradimensions. The obtained results allow us to present an example for unifying six existing flavor quarks, as well as for unifying three existing lepton generators. On the base of the derived charge–mass sum rules, we would predict the existence of some hidden tachyon quarks with fractional charges, as well as some hidden tachyon leptons, neutral or negative charged.

Scalar and spinor fields in signature-changing spacetimes.

The propagation of scalar and spinor fields in a spacetime whose metric changes signature is analyzed. Recent work of Dray et al. on particle production from signature change for a (massless) scalar field is reviewed, and an attempt is made to extend their analysis to the case of a (massless) spin-half field. In contrast to their results for a scalar field, it is shown here---for $SL(2,C)$ spinors---that although there are inequivalent forms of the Dirac equation that can be used to propagate a spinor in a signature changing spacetime, none of these forms gives rise to a conserved inner product on the space of solutions to the field equations.

Scalar fields in a seven-dimensional manifold behaving as Lorentz-covariant spinor fields in space-time

A Lorentz-invariant model of vacuum is given in the form of a 7-dimensional manifold endowed with a statistical metrical tensor. Certain scalar fields on this manifold behave then as spinor fields when viewed from their space-time projection. This paper generalizes previous work fromSO(3)-covariance to Lorentz-covariance.

Scalar field in a seven-dimensional manifold behaving as an SO(3)-covariant spinor field in space-time.

In a Kaluza theory with topology Minkowski-space\ifmmode\times\else\texttimes\fi{}three-sphere, a metrical field equivalent to the Pauli matrices introduces a natural spin structure. Other fields occurring naturally on this manifold behave then as spinor fields when viewed from their space-time projection.

Casimir effect in multiply connected space-time. Massless fields

The vacuum energy density is calculated for all topologically nonequivalent configurations of massive scalar and spinor fields in space-times with topology (S1)2 × R2 and planar metric.

Global spinor fields in space-time

This paper is concerned with space-time manifolds that are space- and time-oriented, causal, and possess spinor structures. Five propositions are proven: (1) If a connected, space- and time-oriented manifold is simply con-nected, then it is non-compact; (2) If such a manifold is simply connected, it admits a spinor structure, which, moreover, is unique; (3) If the space-like section of M is compact, then there exists a global system of orthonormal tetrads on M; (4) The necessary and sufficient condition for every space-time M whose space-like section is compact to admit a spinor structure is that M have a global system of orthonormal tetrads; (5) Every space-time M which can be imbedded in R6 admits a spinor structure. It is further suggested that in view of the fact that the existence of a spinor structure is related to homotopy properties, space-time manifolds may be classified in terms of their homotopy groups πi (M), i=1,2, 3,4. In a concluding section, some avenues for future research are discussed.