Gyromagnetic g_s factors of the spin-1/2 particles in the (1/2+,1/2-,3/2-) triad of the four-vector spinor, psi_mu, irreducibility, and linearity

We show that the spin (1/2-) particle from the (1/2,1)+(1,1/2) Lorentz irreducible sector of the four-vector spinor can not be described within a linear formalism but behaves as a genuinely quadratic fermion satisfying the generalized Feynman-Gell-Mann equation with a gyromagnetic factor of (-2/3). In contrast, spin (1/2 +) from the (1/2,0)+(0,1/2) sector is confirmed as a genuine linear Dirac fermion whose gyromagnetic factor takes the value of two units.We calculate Compton scatterings off each one of the two targets and obtain both times well behaved cross sections in the ultra relativistic limit and in accord with unitarity.

Parity violating effects in an exotic perturbation of the rigid rotator

The perturbation of the free rigid rotator by the trigonometric Scarf potential is shown to conserve its energy excitation patterns and change only the wave functions towards spherical harmonics rescaled by a function of an unspecified parity, or mixtures of such rescaled harmonics of equal magnetic quantum numbers and different angular momenta. In effect, no parity can be assigned to the states of the rotational bands emerging in this exotic way, and the electric dipole operator is allowed to acquire non-vanishing expectation values.

The Higgs oscillator on the hyperbolic plane and Light-Front Holography

The Light Front Holographic (LFH) wave equation, which is the conformal scalar equation on the plane, is revisited from the perspective of the supersymmetric quantum mechanics, and attention is drawn to the fact that it naturally emerges in the small hyperbolic angle approximation to the curved Higgs oscillator on the hyperbolic plane, i.e. on the upper part of the two-dimensional hyperboloid of two sheets, a space of constant negative curvature. Such occurs because the particle dynamics under consideration reduces to the one dimensional Schrodinger equation with the second hyperbolic Poschl-Teller potential, whose flat-space (small-angle) limit reduces to the conformally invariant inverse square distance plus harmonic oscillator interaction, on which LFH is based. In consequence, energies and wave functions of the LFH spectrum can be approached by the solutions of the Higgs oscillator on the hyperbolic plane in employing its curvature and the potential strength as fitting parameters. Also the proton electric charge form factor is well reproduced within this scheme by means of a Fourier-Helgason hyperbolic wave transform of the charge density. In conclusion, in the small angle approximation, the Higgs oscillator on the hyperbolic plane is demonstrated to satisfactory parallel essential outcomes of the Light Front Holographic QCD. The findings are suggestive of associating the hyperboloid curvature of the with a second scale in LFH, which then could be employed in the definition of a chemical potential.

Causal Propagation of Spin-Cascades

We gauge the direct product of the Proca with the Dirac equation that describes the coupling to the electromagnetic field of the spin-cascade (1/2,3/2) residing in the four-vector spinor and analyze propagation of its wave fronts in terms of the Courant-Hilbert criteria. We show that the differential equation under consideration is unconditionally hyperbolic and the propagation of its wave fronts unconditionally causal. In this way we proof that the irreducible spin-cascade embedded within four-vector is free from the Velo-Zwanziger problem that plagues the Rarita-Schwinger description of spin-3/2. The proof extends also to the direct product of two Proca equations and implies causal propagation of the spin-cascade (0,1,2) within an electromagnetic environment.