Application of the photon's intrinsic flux to the 1s‐2p and 2p‐3d excitonic transitions in nanostructures

We have applied our two recent results [depending on its helicity photon carries a quantum flux of ± Φ ₀ = ± hc/e and the quantized magnetic fluxes through the electronic orbits of the Dirac hydrogen atom are given by: Φ (n,l,m_j) = (n‐l‐m_j)Φ₀) ] to the 1s‐2p and 2p‐3d excitonic transitions in nanostructures. It is shown that the flux changes for the non‐zero matrix elements in the 1s‐2p and 2p‐3d excitonic transitions is either ± Φ₀ or zero. The present result supports the previous results stated above. It is also shown that spin flip is possible in the 1s‐2p and 2p‐3d excitonic transitions.     

Cosmological constant from quarks and torsion

We present a simple and natural way to derive the observed small, positive cosmological constant from the gravitational interaction of condensing fermions. In the Riemann‐Cartan spacetime, torsion gives rise to the axial–axial vector four‐fermion interaction term in the Dirac Lagrangian for spinor fields. We show that this nonlinear term acts like a cosmological constant if these fields have a nonzero vacuum expectation value. For quark fields in QCD, such a torsion‐induced cosmological constant is positive and its energy scale is only about 8 times larger than the observed value. Adding leptons to this picture could lower this scale to the observed value.     

Relativistic particles on quantum space-time

We discuss alternatives to the usual quantization of a relativistic particle which result in discrete spectra for position and time operators.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

On Fuzzy Probability Theory

Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition.     

S-wave baryons in an equally mixed scalar-vector square root potential model of independent quarks

A relativistic model of independent quarks based on Dirac equation with an equally mixed scalar-vector square root confining potential is used to compute the quark core contributions to the static properties like magnetic moments, charge radii and axial vector coupling constant ratios of the baryon octet. The results obtained with appropriate corrections due to centre-of-mass motion agree fairly well with experimental values. The model is also extended to the study of magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors and the overall predictions so obtained compare well with other model predictions.     

Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

Isospin-dependent relativistic microscopic optical potential in the Dirac Brueckner-Hartree-Fock method

There is growing evidence to suggest that the binding energy of nucleon in nuclear matter comes from a cancellation between large Lorentz scalar and vector potentials[1,2]. The relativistic approach has been of a great success in describing not only the ground state properties of stable nuclei, but also those of exotic nuclei. In the relativistic frame, the spin-orbit coupling can be deduced automatically, which is usually given by hand in the non-relativistic approach. The relativistic method…