scholarly journals Dirac Particles in the Minkowski Space with Torsion

1978 ◽  
Vol 31 (2) ◽  
pp. 195 ◽  
Author(s):  
MP O'Connor ◽  
PK Smrz
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Covariant Derivative ◽  
Dirac Spinor ◽  
Simple Derivation ◽  
Minkowski Metric ◽  
Dirac Particles ◽  
Straight Line ◽  
Constant Torsion

After presenting a simple derivation of the covariant derivative of the Dirac spinor functions, the Dirac equation in the space of constant torsion, Minkowski metric and straight line geodesics is considered. Solutions of the equation are given, showing the particular way in which the energy degeneracy of the states with different spin projections is removed in the presence of torsion.

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 DIRAC SPINOR IN A NONSTATIONARY GÖDEL-TYPE COSMOLOGICAL UNIVERSE

1993 ◽  
Vol 08 (32) ◽  
pp. 3011-3015 ◽  
Author(s):  
VÍCTOR M. VILLALBA
Keyword(s):  
Dirac Equation ◽  
Frequency Spectrum ◽  
Rotational Speed ◽  
Separation Of Variables ◽  
Dirac Spinor ◽  
Dirac Particles

In this letter we solve, via separation of variables, the massless Dirac equation in a nonstationary rotating, causal Gödel-type cosmological universe, having a constant rotational speed in all the points of the space. We compute the frequency spectrum. We show that the spectrum of massless Dirac particles is discrete and unbounded.

scholarly journals LANDAU EQUATIONS AND ASYMPTOTIC OPERATION

1999 ◽  
Vol 14 (05) ◽  
pp. 683-715 ◽  
Author(s):  
F. V. TKACHOV
Keyword(s):  
Minkowski Space ◽  
Feynman Diagrams ◽  
Simple Derivation ◽  
Wave Fronts ◽  
Theoretic Technique ◽  
Singular Wave

The pinched/nonpinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities, for example due to linear denominators in non-covariant gauges, etc. As another application, the results of Euclidean asymptotic operation are extended to a class of quasi-Euclidean asymptotic regimes in Minkowski space.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

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.

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.

scholarly journals Trajectory construction of Dirac evolution

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190682
Author(s):  
Peter Holland
Keyword(s):  
Dirac Equation ◽  
Evolution Operator ◽  
Exact Formula ◽  
Dirac Spinor ◽  
Mean Flow ◽  
First Order ◽  
Continuity Equations ◽  
The Mean ◽  
Trajectory Models ◽  
Mass Dependent

We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which the real and imaginary parts of the wave function, angular versions of Majorana spinors, define conserved densities. We hence deduce an exact formula for the propagation of the Dirac spinor derived from the self-contained first-order dynamics of two sets of trajectories in 3-space together with a mass-dependent evolution operator. The Lorentz covariance of the trajectory equations is established by invoking the ‘relativity of the trajectory label'. We show how these results extend to the inclusion of external potentials. We further show that the angular version of Dirac's equation implies continuity equations for currents with non-negative densities, for which the Dirac current defines the mean flow. This provides an alternative trajectory construction of free evolution. Finally, we examine the polar representation of the Dirac equation, which also implies a non-negative conserved density but does not map into a stand-alone trajectory theory. It reveals how the quantum potential is tacit in the Dirac equation.

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.

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