scholarly journals Emergence of complex and spinor wave functions in scale relativity. I. Nature of scale variables

2013 ◽  
Vol 54 (11) ◽  
pp. 112102 ◽  
Author(s):  
Laurent Nottale ◽  
Marie-Noëlle Célérier
Keyword(s):  
Wave Functions ◽  
Scale Relativity ◽  
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 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.

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.

scholarly journals Pseudo-spin Symmetry in Dirac-Four-Parameter Diatomic Problem Coupled with a Coulomb-like Tensor potential

BIBECHANA ◽  
2012 ◽  
Vol 8 ◽  
pp. 23-30
Author(s):  
Mahdi Eshghi
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Tensor Potential ◽  
Uvarov Method ◽  
Spinor Wave

In this work, we use the parametric generalization of the Nikiforov-Uvarov method to obtain the relativistic bound state energy spectrum and the corresponding spinor wave-functions for four-parameter diatomic potential coupled with a Coulomb-like tensor under the condition of the pseudo-spin symmetry. Also, some numerical results have given.Keywords: Dirac equation; four-parameter diatomic potential; Coulomb-like tensorDOI: http://dx.doi.org/10.3126/bibechana.v8i0.4879BIBECHANA 8 (2012) 23-30

GRASSMANN WAVE FUNCTIONS AND INTRINSIC SPIN

1988 ◽  
Vol 03 (03) ◽  
pp. 591-602 ◽  
Author(s):  
R. DELBOURGO
Keyword(s):  
Angular Momentum ◽  
Dirac Equation ◽  
Spherical Harmonics ◽  
Wave Functions ◽  
Orbital Momentum ◽  
Spin Angular Momentum ◽  
Relativistic Generalization ◽  
Spinor Wave ◽  
Complete Analogy

By associating spin angular momentum with Sp(2) transformations on two Grassmann coordinates, we show how one may formulate spinor wave functions in complete analogy to spherical harmonics for orbital momentum. The relativistic generalization requires a doubling of Grassmann coordinates and a connection may be established with the Dirac equation.

Relativistic symmetries of fermions in the background of the inversely quadratic Yukawa potential with Yukawa potential as a tensor

2014 ◽  
Vol 92 (1) ◽  
pp. 51-58
Author(s):  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Yukawa Potential ◽  
Bound State ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Yukawa Tensor Interaction ◽  
Uvarov Method ◽  
Spinor Wave ◽  
Component Spinor

In the presence of spin and pseudo-spin symmetries, we obtain approximate analytical bound state solutions to the Dirac equation with scalar–vector inverse quadratic Yukawa potential including a Yukawa tensor interaction for any arbitrary spin–orbit quantum number, κ. The energy eigenvalues and their corresponding two-component spinor wave functions are obtained in closed form using the parametric Nikiforov–Uvarov method. It is noticed that the tensor interaction removes the degeneracy in the spin and p-spin doublets. Some numerical results are obtained for the lowest energy states within spin and pseudo-spin symmetries.

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