scholarly journals Inverse approach to solutions of the Dirac equation for space-time dependent fields

2015 ◽  
Vol 92 (2) ◽  
Author(s):  
Johannes Oertel ◽  
Ralf Schützhold
Keyword(s):  
Dirac Equation ◽  
Space Time ◽  
Time Dependent ◽  
Inverse Approach

scholarly journals An exact solution of the Dirac equation for a time-dependent Hamiltonian in 1-1 dimension space-time

2010 ◽  
Vol 88 (2) ◽  
pp. 137-138 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Space Time ◽  
Time Dependent ◽  
Dependent Potential ◽  
Dimension Space

We find an exact solution to the Dirac equation in 1–1 dimension space-time in the presence of a time-dependent potential that consists of a combination of electric, scalar, and pseudoscalar terms.

scholarly journals Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Özlem Yeşiltaş
Keyword(s):  
Dirac Equation ◽  
Three Dimensional ◽  
Space Time ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Metric Tensor ◽  
Curved Space ◽  
Dimensional Gravity ◽  
Dirac Hamiltonian

The Dirac Hamiltonian in the(2+1)-dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is two spheres. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudosupersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is generated. Usingη-pseudo-Hermiticity, the intertwining operator connecting the non-Hermitian Hamiltonians to the Hermitian counterparts is found. We have obtained a new metric tensor related to the new Hamiltonian.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

Exact solutions of Dirac equation on a static curved space–time

2019 ◽  
Vol 401 ◽  
pp. 21-39 ◽  
Author(s):  
M.D. de Oliveira ◽  
Alexandre G.M. Schmidt
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Space Time ◽  
Curved 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.

De la combinatoire du modèle de l'échiquier de Feynman et des fonctions spéciales

1984 ◽  
Vol 62 (7) ◽  
pp. 632-638
Author(s):  
J. G. Williams
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Hypergeometric Series ◽  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Continuous Limit ◽  
Two Dimensional ◽  
Dimensional Space Time

The exact solution of the Feynman checkerboard model is given both in terms of the hypergeometric series and in terms of Jacobi polynomials. It is shown how this leads, in the continuous limit, to the Dirac equation in two-dimensional space-time.

scholarly journals Evolution of a domain wall in expanding universe: inflation and after it

2018 ◽  
Vol 191 ◽  
pp. 08004
Author(s):  
A.D. Dolgov ◽  
S.I. Godunov ◽  
A.S. Rudenko
Keyword(s):  
Domain Wall ◽  
Hubble Parameter ◽  
Domain Walls ◽  
Flat Space ◽  
Space Time ◽  
Time Dependent ◽  
Expanding Universe ◽  
Large Size ◽  
Dependent Parameter ◽  
Thick Domain Walls

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.

New Routines for Algebraic Programming of the Dirac Equation

1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov
Keyword(s):  
Dirac Equation ◽  
Main Part ◽  
Space Time ◽  
Curved Space ◽  
Algebraic Programming ◽  
Matrix Algebras ◽  
Dirac Matrix ◽  
New Procedures

We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.

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