GENERALIZED VOLKOV PROBLEM

1991 ◽  
Vol 06 (27) ◽  
pp. 4831-4841
Author(s):  
GERMAN V. SHISHKIN ◽  
MOHAMMED A. YASIN
Keyword(s):  
Dirac Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
Wave Fields ◽  
Cartesian Coordinates ◽  
First Order ◽  
Minkowski Space Time ◽  
External Wave

We consider the Dirac equation in Minkowski space-time in Cartesian coordinates with external wave fields of different tensor structures, namely in the presence of scalar, vector, pseudoscalar, pseudovector, coupled vector and tensor, and coupled vector and pseudovector waves, i.e. we consider the generalized Volkov problem. The solution of the Dirac equation is reduced to that of a system of four equations, two of which are first-order ordinary differential equations and two are algebraic ones. Series of new solutions of the Dirac equation are obtained.

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 A New Method for Inextensible Flows of Timelike Curves in Minkowski Space-Time E14

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
New Method ◽  
Frenet Frame ◽  
Partial Differential ◽  
Minkowski Space Time ◽  
Inextensible Flows ◽  
The Given

We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.

scholarly journals MAPPING CARTESIAN COORDINATES INTO EMISSION COORDINATES: SOME TOY MODELS

2008 ◽  
Vol 17 (02) ◽  
pp. 311-326 ◽  
Author(s):  
MATTEO LUCA RUGGIERO ◽  
ANGELO TARTAGLIA
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Space Time ◽  
Cartesian Coordinates ◽  
Positioning Systems ◽  
Minkowski Space Time ◽  
Relativistic Approach ◽  
Small Inhomogeneity

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for a suitably chosen set of emitters, whose world lines are supposed to be known by the users. We consider Minkowski space–time and the space–time where a small inhomogeneity is introduced (i.e. a small a "gravitational" field), in 1 + 1 and 1 + 3 dimensions.

scholarly journals THE DIRAC–HESTENES EQUATION FOR SPHERICAL SYMMETRIC POTENTIALS IN THE SPHERICAL AND CARTESIAN GAUGES

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4071-4082 ◽  
Author(s):  
ROLDÃO DA ROCHA ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Spherical Symmetry ◽  
Separation Of Variables ◽  
Differential Forms ◽  
Space Time ◽  
Minkowski Space Time ◽  
Clifford Bundle

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space–time the Dirac–Hestenes equation — which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation — by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac–Hestenes equation in both gauges has exactly the same mathematical difficulty.

Landau levels from noncommutative U(1)⋆ gauge theory in κ-Minkowski space-time

2018 ◽  
Vol 15 (08) ◽  
pp. 1850141
Author(s):  
Marija Dimitrijević Ćirić ◽  
Nikola Konjik
Keyword(s):  
Minkowski Space ◽  
Energy Levels ◽  
Quantum Hall ◽  
Space Time ◽  
Perturbative Approach ◽  
Gauge Transformations ◽  
First Order ◽  
Lowest Landau Level ◽  
Minkowski Space Time ◽  
Background Magnetic Field

Motivated by physics of the Lowest Landau Level and the Quantum Hall Effect, we investigate motion of an electron in a constant background magnetic field in the [Formula: see text]-Minkowski space-time. Starting from an action invariant under the noncommutative [Formula: see text] gauge transformations, we obtain the [Formula: see text]-deformed Dirac equation. Using the perturbative approach, we calculate noncommutative corrections to energy levels, mass and the gyromagnetic ratio up to the first order in the deformation parameter [Formula: see text].

LIFETIME OF A DE SITTER PARTICLE

2008 ◽  
Vol 05 (08) ◽  
pp. 1243-1254
Author(s):  
HENRI EPSTEIN
Keyword(s):  
Perturbation Theory ◽  
Minkowski Space ◽  
Principal Series ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Complementary Series ◽  
First Order ◽  
Interaction Terms ◽  
Minkowski Space Time

The familiar rule which, in Minkowski space-time, forbids the decay of a particle into heavier products, does not hold in de Sitter space-time. We study, in first order of perturbation theory, the decay of a particle of the "principal series" and show that it may decay into two particles of any of the "principal" or "complementary" series (with suitable interaction terms). Spectral conditions reappear in the decay of a "complementary" particle: but its lifetime is 0.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time
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