scholarly journals Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Sami Boudieb ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Abelian Field ◽  
The Green Function

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

Green’s function for an electron model with a plane wave

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Hassen Ould Lahoucine ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Plane Wave ◽  
Path Integral ◽  
Equations Of Motion ◽  
Free Particle ◽  
Dirac Particle ◽  
Integral Approach ◽  
Electron Model ◽  
Plane Wave Field ◽  
The Green Function

AbstractThe Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.

scholarly journals Dirac Particle in External Non-Abelian Gauge Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bilel Hamil ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Gauge Field ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Formalism ◽  
Abelian Gauge ◽  
Lorentz Gauge ◽  
Path Integral Formalism ◽  
The Green Function

The Green function of a Dirac particle in interaction with a non-Abelian SU(N) gauge field exactly and analytically determined via the path integral formalism by using the approach so-called “global projection.” The essential steps in the calculation are the choice of a convenient gauge (Lorentz gauge) and the introduction of two constraints, φ=kx (related to space) and Grassmannian η=kψ (related to Dirac matrices). Furthermore, it is shown that certain selected equations obtained during the integrations can also be classically derived.

On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle

2015 ◽  
Vol 6 (3) ◽  
Author(s):  
Makhmud A. Sadybekov ◽  
Batirkhan K. Turmetov ◽  
Berikbol T. Torebek
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Unit Ball ◽  
Explicit Form ◽  
Laplace Operator ◽  
Green's Function ◽  
Robin Problem ◽  
The Green Function ◽  
The Laplace Operator

AbstractThe paper is devoted to investigation questions about constructing the explicit form of the Green's function of the Robin problem in the unit ball of ℝ

Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

2022 ◽  
Author(s):  
A. Merdaci ◽  
N. Boudiaf ◽  
L. Chetouani
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Spin Dynamics ◽  
Coulomb Field ◽  
Dirac Particle ◽  
Coordinate Space ◽  
Relativistic Limit ◽  
Integral Treatment ◽  
Aharonov Bohm

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

On Green’s function of the Robin problem for the Poisson equation

2019 ◽  
Vol 10 (3) ◽  
pp. 203-213 ◽  
Author(s):  
Valery V. Karachik ◽  
Batirkhan K. Turmetov
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Unit Ball ◽  
Poisson Equation ◽  
Green's Function ◽  
Explicit Representation ◽  
Robin Problem ◽  
The Poisson Equation ◽  
The Green Function

AbstractAn explicit representation of the Green function of the Robin problem for the Poisson equation in the unit ball is given.

Propagation of a Dirac particle. A path integral approach

1984 ◽  
Vol 25 (6) ◽  
pp. 1810-1819 ◽  
Author(s):  
Takashi Ichinose ◽  
Hiroshi Tamura
Keyword(s):  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach
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