scholarly journals Towards the Unification of All Interactions (The First Part: The Spinor Wave)

2016 ◽  
Vol 07 (12) ◽  
pp. 1568-1590 ◽  
Author(s):  
Claude Daviau ◽  
Jacques Bertrand ◽  
Dominique Girardot
Keyword(s):  
Spinor Wave

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals Geometrical interpretation of the pilot wave theory and manifestation of spinor fields

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mariya Iv. Trukhanova ◽  
Gennady Shipov
Keyword(s):  
Wave Theory ◽  
Geometrical Interpretation ◽  
Real Field ◽  
Spin Vector ◽  
Spinor Wave Function ◽  
Spinning Particle ◽  
Pilot Wave ◽  
Intrinsic Angular Momentum ◽  
Spinor Wave ◽  
Pilot Wave Theory

Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.

scholarly journals Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

2014 ◽  
Vol 69 (3-4) ◽  
pp. 163-172 ◽  
Author(s):  
Altuğ Arda ◽  
Ramazan Sever
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
K Value ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Hellmann Potential ◽  
Uvarov Method ◽  
Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

scholarly journals Canonical formalism and quantization of a massless spinning bosonic particle in four dimensions

2014 ◽  
Vol 29 (08) ◽  
pp. 1450044 ◽  
Author(s):  
Shinichi Deguchi ◽  
Shouma Negishi ◽  
Satoshi Okano ◽  
Takafumi Suzuki
Keyword(s):  
Minkowski Space ◽  
Canonical Formalism ◽  
Wave Functions ◽  
Dimensional Parameter ◽  
Spinning Particle ◽  
Plane Wave Solution ◽  
Four Dimensions ◽  
Constrained Hamiltonian Systems ◽  
Dimensional Minkowski Space ◽  
Spinor Wave

A twistor model of a free massless spinning particle in four-dimensional Minkowski space is studied in terms of space–time and spinor variables. This model is specified by a simple action, referred to here as the gauged Shirafuji action, that consists of twistor variables and gauge fields on the one-dimensional parameter space. We consider the canonical formalism of the model by following the Dirac formulation for constrained Hamiltonian systems. In the subsequent quantization procedure, we obtain a plane-wave solution with momentum spinors. From this solution and coefficient functions, we construct positive-frequency and negative-frequency spinor wave functions defined on complexified Minkowski space. It is shown that the Fourier–Laplace transforms of the coefficient functions lead to the spinor wave functions expressed as the Penrose transforms of the corresponding holomorphic functions on twistor space. We also consider the exponential generating function for the spinor wave functions and derive a novel representation for each of the spinor wave functions.

Homotopy construction of a spinor wave functional

1983 ◽  
Vol 22 (11) ◽  
pp. 981-996
Author(s):  
P. L. Antonelli ◽  
J. G. Williams
Keyword(s):  
Spinor Wave

scholarly journals SOLUTION OF THE DIRAC EQUATION WITH NONCENTRAL THREE-VECTOR POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 581-592 ◽  
Author(s):  
A. D. ALHAIDARI
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Vector Potential ◽  
Radial Component ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Dirac Oscillator ◽  
Spherical Coordinates ◽  
The One ◽  
Spinor Wave

We introduce coupling to three-vector potential in the (3+1)-dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wave functions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The coupling presented in this work is a generalization of the one which was introduced by Moshinsky and Szczepaniak for the Dirac-oscillator problem.

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