The Dirac Equation and the Dirac Field

1990 ◽  
pp. 55-79
Author(s):  
Otto Nachtmann
Keyword(s):  
Dirac Equation ◽  
Dirac Field

scholarly journals COULOMB SCATTERING OF THE DIRAC FERMIONS ON DE SITTER EXPANDING UNIVERSE

2007 ◽  
Vol 22 (34) ◽  
pp. 2573-2585 ◽  
Author(s):  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Cross Section ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
De Sitter Spacetime ◽  
Dirac Fermions ◽  
Final States ◽  
De Sitter ◽  
Sitter Spacetime

The lowest order contribution of the amplitude of the Dirac–Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given momentum and helicity. One studies the difficulties that arises when one passes from the amplitude to cross section.

Dirac Field, Gravity, Inertial Effects, and Computer Algebra

1997 ◽  
Vol 08 (02) ◽  
pp. 345-359 ◽  
Author(s):  
Dumitru N. Vulcanov ◽  
Ion I. Cotăescu
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Reference Frame ◽  
Computer Algebra ◽  
Dirac Field ◽  
Inertial Reference Frame ◽  
Inertial Effects ◽  
Algebraic Programming ◽  
Relativistic Approximation

The article presents some new results obtained for the non-relativistic approximation of the Dirac equation in a non-inertial reference frame — rotated and accelerated — and in Schwarzschild gravitational field. These results are obtained with new routines of algebraic programming in REDUCE + EXCALC language for the Dirac equation in a non-inertial reference frame and after three successive Foldy–Wouthuysen transformations.

DIRAC FIELD IN THE FIVE-DEMENSIONAL KALUZA-KLEIN THEORY WITH SCALAR FIELD

1992 ◽  
Vol 07 (21) ◽  
pp. 5105-5113 ◽  
Author(s):  
A. MACÍAS ◽  
H. DEHNEN
Keyword(s):  
Scalar Field ◽  
Dirac Equation ◽  
Ground State ◽  
Mass Term ◽  
Dirac Field ◽  
Electron Mass ◽  
Dimensional Theory ◽  
Klein Theory ◽  
Kaluza Klein

In this work we investigate the five-dimensional Kaluza-Klein theory with a scalar field contained in the metric, where a Dirac-field is coupled to the metric field. We find that in the four-dimensional theory a nontrivial ground state for the scalar field exists and therefore the mass term in the Dirac equation can be interpreted, for example, as the electron mass.

scholarly journals REMARKS ON THE SPHERICAL WAVES OF THE DIRAC FIELD ON de SITTER SPACETIME

2006 ◽  
Vol 21 (16) ◽  
pp. 1313-1318 ◽  
Author(s):  
ION I. COTĂESCU ◽  
RADU RACOCEANU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Dirac Field ◽  
De Sitter Spacetime ◽  
Moving Frames ◽  
De Sitter ◽  
Spherical Waves ◽  
Commuting Operators ◽  
Quantum Numbers ◽  
Sitter Spacetime

The Shishkin's solutions of the Dirac equation in spherical moving frames of the de Sitter spacetime are investigated pointing out the set of commuting operators whose eigenvalues determine the integration constants. It is shown that these depend on the usual angular quantum numbers and, in addition, on the value of the scalar momentum. With these elements a new result is obtained finding the system of solutions normalized (in generalized sense) in the scale of scalar momentum.

scholarly journals DIRAC–COULOMB SCATTERING WITH PLANE WAVE ENERGY EIGENSPINORS ON DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (09) ◽  
pp. 1351-1359 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Wave Energy ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
Final States ◽  
De Sitter ◽  
Scattering Process

The lowest order contribution of the amplitude of Dirac–Coulomb scattering in de Sitter space–time is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter space–time with a given energy and helicity. We find that the total energy is conserved in the scattering process.

scholarly journals Time evolution of the free Dirac field in spatially flat FLRW space–times

2020 ◽  
Vol 35 (32) ◽  
pp. 2030019
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Dirac Equation ◽  
Rest Frame ◽  
Relativistic Quantum ◽  
Fundamental Solutions ◽  
Relativistic Quantum Mechanics ◽  
Dirac Field ◽  
De Sitter ◽  
Spherical Waves ◽  
New Type ◽  
First Time

The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional adiabatic one or as the rest frame vacuum we proposed recently. All the known solutions of the Dirac equation on these manifolds are discussed in all details and a new type of spherical waves of given energy in the de Sitter expanding universe is reported here for the first time.

ELECTRODYNAMICS OF THE DIRAC FIELD

1988 ◽  
Vol 03 (02) ◽  
pp. 139-145
Author(s):  
G. PAPINI
Keyword(s):  
Dirac Equation ◽  
Maxwell Equations ◽  
Scalar Fields ◽  
Dirac Field ◽  
Vector Bosons

Classical electrodynamical models are constructed in which both vector bosons and fermions are generated by massless, topologically singular scalar fields. The Dirac equation supplies Maxwell equations and the constraint necessary to obtain from them charged fermions with stringlike structure.

scholarly journals DISCRETE QUANTUM MODES OF THE DIRAC FIELD IN AdSd+1 BACKGROUNDS

2004 ◽  
Vol 19 (14) ◽  
pp. 2217-2232 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
Dirac Equation ◽  
Simple Form ◽  
Isometry Group ◽  
Energy Levels ◽  
Free Field ◽  
Dirac Field ◽  
Spherically Symmetric ◽  
Spherical Coordinates ◽  
Cartesian Coordinates ◽  
Special Version

It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the Dirac free field in AdS d+1 backgrounds is analytically solved obtaining the formula of the energy levels and the corresponding normalized eigenspinors.

scholarly journals Quantization of κ-deformed Dirac equation

2020 ◽  
Vol 35 (25) ◽  
pp. 2050147
Author(s):  
E. Harikumar ◽  
Vishnu Rajagopal
Keyword(s):  
Dirac Equation ◽  
Particle Physics ◽  
Equations Of Motion ◽  
Space Time ◽  
Dirac Field ◽  
Oscillator Algebra ◽  
First Order ◽  
Deformed Oscillator Algebra ◽  
Mass Dependent ◽  
Conserved Currents

In this paper, we study the quantization of Dirac field theory in the [Formula: see text]-deformed space–time. We adopt a quantization method that uses only equations of motion for quantizing the field. Starting from [Formula: see text]-deformed Dirac equation, valid up to first order in the deformation parameter [Formula: see text], we derive deformed unequal time anticommutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anticommutation relations between [Formula: see text]-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the [Formula: see text]-deformed conserved currents, valid up to first order in [Formula: see text], corresponding to parity and time-reversal symmetries of [Formula: see text]-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in [Formula: see text]. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its antiparticle satisfy different equations in [Formula: see text] space–time.

scholarly journals Quasibound states of the Dirac field in Schwarzschild and Reissner–Nordström black hole backgrounds

2019 ◽  
Vol 34 (39) ◽  
pp. 1950323 ◽  
Author(s):  
Ciprian A. Sporea
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dirac Equation ◽  
Bound States ◽  
Quantization Condition ◽  
Coulomb Energy ◽  
Dirac Field ◽  
Black Hole Mass ◽  
Quasibound State ◽  
Good Agreement

In this paper, we study the existence of (quasi)bound states in two spacetime geometries describing Schwarzschild and Reissner–Nordström black holes. For obtaining these types of states, we search for discrete quantum modes of the massive Dirac equation in the two geometries. After imposing the quantization condition, an analytical expression for the energy of the ground states is derived. The energy of higher states is then obtained numerically. For very small values of the black hole mass M, we compare the energy of the Reissner–Nordström black hole quasibound state with the Dirac–Coulomb energy and we have found the two to be in good agreement.

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