scholarly journals Dirac Particles in Coulomb Like Field in FLRW–Space

2021 ◽  
Vol 14 (14) ◽  
pp. 1-5
Author(s):  
S. K. Sharma ◽  
P. R. Dhungel ◽  
U. Khanal
Keyword(s):  
Dirac Equation ◽  
Effective Potential ◽  
Electric Potential ◽  
Maxwell Equations ◽  
Dirac Particle ◽  
Legendre Functions ◽  
Dirac Particles ◽  
Angular Part ◽  
Vector Potentials ◽  
Temporal Parts

Behaviour of the Dirac particle in Coulomb like field in FLRW space is investigated. Firstly, the Maxwell equations, in terms of the vector potentials are solved to identify the Lorentz and Coulomb like gauges.  The radial Coulomb like potential is solved in terms of Legendre functions. Then the Dirac equation is generalized to include this potential and the angular part is separated and solved. The radial and temporal parts of the mass less case is also separated and solved. But the massive case remains coupled. This is still reduced to the case where the Dirac particle can be represented as being in a combined gravitational and electric potential. This effective potential is found to develop an attractive well, which may require a revisit to the recombination era.

scholarly journals The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Souma Jinno ◽  
Shuji Kitora ◽  
Hiroshi Toki ◽  
Masayuki Abe
Keyword(s):  
Numerical Method ◽  
Time Domain ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
New Formalism ◽  
Vector Potentials ◽  
Lumped Parameter ◽  
Radiation Theory ◽  
Stable Solutions ◽  
The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

Approximate treatment of the Dirac equation with scalar and vector potentials of rectangular shapes

1994 ◽  
Vol 50 (1) ◽  
pp. 29-33 ◽  
Author(s):  
M. E. Grypeos ◽  
C. G. Koutroulos ◽  
G. J. Papadopoulos
Keyword(s):  
Dirac Equation ◽  
Vector Potentials ◽  
Approximate Treatment

scholarly journals INFLUENCE OF GRAVITY ON NONCOMMUTATIVE DIRAC EQUATION

2005 ◽  
Vol 20 (26) ◽  
pp. 1997-2005 ◽  
Author(s):  
SOFIANE BOUROUAINE ◽  
ACHOUR BENSLAMA
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Covariant Derivative ◽  
Strong Electric Field ◽  
Curved Spacetime ◽  
Tetrad Formalism ◽  
Dirac Particles ◽  
Modified Dirac Equation ◽  
New Form

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.

scholarly journals High energy scattering of Dirac particles on smooth potentials

2016 ◽  
Vol 31 (23) ◽  
pp. 1650126 ◽  
Author(s):  
Nguyen Suan Han ◽  
Le Anh Dung ◽  
Nguyen Nhu Xuan ◽  
Vu Toan Thang
Keyword(s):  
Dirac Equation ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Type Representation ◽  
Dirac Particles ◽  
Energy Scattering ◽  
Two Component ◽  
High Energy Scattering

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy–Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

Dirac particle in electric field with confining scalar potential on (anti)-de Sitter background

2018 ◽  
Vol 33 (34) ◽  
pp. 1850202 ◽  
Author(s):  
N. Messai ◽  
B. Hamil ◽  
A. Hafdallah
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Electric Field ◽  
Scalar Potential ◽  
Dirac Particle ◽  
Wave Functions ◽  
De Sitter ◽  
Sitter Background ◽  
Position Representation

In this paper, we study the (1 + 1)-dimensional Dirac equation in the presence of electric field and scalar linear potentials on (anti)-de Sitter background. Using the position representation, the energy spectrum and the corresponding wave functions are exactly obtained.

scholarly journals Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850186 ◽  
Author(s):  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Negative Energy ◽  
Dirac Particle ◽  
Relativistic Quantum Mechanics ◽  
Probability Current ◽  
Negative Probability

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

A solvable two-body Dirac equation in one space dimension

1991 ◽  
Vol 69 (7) ◽  
pp. 780-785 ◽  
Author(s):  
F. Dominguez-Adame ◽  
B. Méndez
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Space Dimension ◽  
Translational Motion ◽  
Effective Frequency ◽  
Klein Paradox ◽  
Independent Components ◽  
Dirac Particles ◽  
One Space Dimension

A solvable Hamiltonian for two Dirac particles interacting by instantaneous linear potentials in (1 + 1) dimensions is discussed. The system presents no Klein paradox even if the coupling is rather strong, so particles remain bound. The four independent components of the wave function describing the system resemble the nonrelativistic oscillator eigenfunctions. Although the Hamiltonian is not fully covariant, the effective frequency of the oscillator obeys a typical relativistic Doppler law. In contrast to the nonrelativistic treatment, eigenstates are intrinsically coupled with the overall translational motion of the system.

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