Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

White Noise Path Integral Treatment of a Two-dimensional Dirac Oscillator in a Uniform Magnetic Field

2008 ◽  
Author(s):  
Lyndon D. Bastatas ◽  
Jinky B. Bornales ◽  
Christopher C. Bernido ◽  
M. Victoria Carpio-Bernido
Keyword(s):  
Magnetic Field ◽  
White Noise ◽  
Path Integral ◽  
Uniform Magnetic Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Integral Treatment

Path integral treatment for the one‐dimensional Natanzon potentials

1993 ◽  
Vol 34 (4) ◽  
pp. 1257-1269 ◽  
Author(s):  
L. Chetouani ◽  
L. Guechi ◽  
A. Lecheheb ◽  
T. F. Hammann
Keyword(s):  
Path Integral ◽  
One Dimensional ◽  
Integral Treatment ◽  
The One

PARTITION FUNCTIONS OF THE SUPERCONFORMAL GHOST THIRRING MODEL

1989 ◽  
Vol 04 (20) ◽  
pp. 5553-5574 ◽  
Author(s):  
D. Z. FREEDMAN ◽  
K. PILCH
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Formal Series ◽  
Open String ◽  
Integral Representations ◽  
Thirring Model ◽  
Partition Functions ◽  
First Order ◽  
Integral Methods ◽  
The One

The one-loop partition functions of the superconformal Thirring model for first order b − c and β − γ ghost fields are studied for both closed and open string boundary conditions. Bosonized partition functions are given by formal series which usually diverge because the energy spectrum of the theory is unbounded below as a correlate of nonunitarity. However, the same partition functions are then calculated by path integral methods directly in the fermionic formulation, and well-defined (convergent) integral representations are obtained. A formal series expansion of those integrals reproduces the bosonized partition functions.

CONSTRAINED FERMIONIC MODELS IN NON-TRIVIAL TOPOLOGICAL SECTORS

1992 ◽  
Vol 07 (24) ◽  
pp. 2179-2188 ◽  
Author(s):  
ENRIQUE F. MORENO
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Coulomb Gas ◽  
Effective Theory ◽  
Fermionic Model ◽  
Topological Sector ◽  
Integral Treatment ◽  
Background Charge

We study a constrained fermionic model involving non-trivial topological gauge configurations. After a path-integral treatment of the topologically trivial degrees of freedom we show that the resulting effective theory is equivalent to a Coulomb gas theory with a "background charge" at infinity plus a b, c ghost system. The Virasoro central charge of the theory is found to be independent of the topological sector.

scholarly journals The Stark effect with minimum length

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750010 ◽  
Author(s):  
H. L. C. Louzada ◽  
H. Belich
Keyword(s):  
Perturbation Theory ◽  
Energy Spectrum ◽  
Hydrogen Atom ◽  
Electric Field ◽  
Stark Effect ◽  
Heisenberg Algebra ◽  
Uniform Electric Field ◽  
Minimum Length

We will study the splitting in the energy spectrum of the hydrogen atom subjected to an uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate (n[Formula: see text]=[Formula: see text]1) and degenerate (n[Formula: see text]=[Formula: see text]2), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.

scholarly journals SOLUTION OF THE DIRAC EQUATION WITH NONCENTRAL THREE-VECTOR POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 581-592 ◽  
Author(s):  
A. D. ALHAIDARI
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Vector Potential ◽  
Radial Component ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Dirac Oscillator ◽  
Spherical Coordinates ◽  
The One ◽  
Spinor Wave

We introduce coupling to three-vector potential in the (3+1)-dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wave functions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The coupling presented in this work is a generalization of the one which was introduced by Moshinsky and Szczepaniak for the Dirac-oscillator problem.

Effect of Quincke Rotation and Taylor Circulation on Mass Transfer from a Fluid Drop in a Constant Electric Field

2011 ◽  
Vol 312-315 ◽  
pp. 259-264
Author(s):  
Tov Elperin ◽  
A. Fominykh
Keyword(s):  
Mass Transfer ◽  
Electric Field ◽  
Similarity Transformation ◽  
Constant Electric Field ◽  
Analytical Form ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Convective Mass Transfer ◽  
Fluid Drop ◽  
Quincke Rotation

We consider non-stationary convective mass transfer in a binary system comprising a stationary dielectric two-dimensional fluid drop embedded into an immiscible dielectric liquid under the influence of a constant uniform electric field. The partial differential equation of diffusion is solved by means of a similarity transformation, and the solution is obtained in a closed analytical form. Dependence of Sherwood number vs. the strength of the applied electric field is analyzed. It is shown that an electric field can be used for enhancement of the rate of mass transfer in terrestrial and reduced gravity environments.

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