Dirac Particle in a Constant Magnetic Field: Path Integral Treatment

2008 ◽  
Vol 63 (5-6) ◽  
pp. 283-290 ◽  
Author(s):  
Abdeldjalil Merdaci ◽  
Nadira Boudiaf ◽  
Lyazid Chetouani
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Dirac Particle ◽  
Wave Functions ◽  
Green Functions ◽  
Integral Treatment ◽  
Global And Local

The Green functions related to a Dirac particle in a constant magnetic field are calculated via two methods, global and local, by using the supersymmetric formalism of Fradkin and Gitman. The energy spectrum as well as the corresponding wave functions are extracted following these two approaches.

Path Integral Treatment of a Dirac Particle in a Weak Gravitational Plane Wave

2010 ◽  
Vol 65 (5) ◽  
pp. 431-444
Author(s):  
Sana Zabat ◽  
Lyazid Chetouani
Keyword(s):  
Gravitational Field ◽  
Path Integral ◽  
Dirac Particle ◽  
Green Functions ◽  
Integral Formalism ◽  
Dirac Particles ◽  
Weak Gravitational Field ◽  
Klein Gordon ◽  
Integral Treatment ◽  
Classical Trajectories

The Green functions for Klein-Gordon and Dirac particles in a weak gravitational field are determined exactly by the path integral formalism. By using simple changes, it is shown that the classical trajectories play an important role in determining these Green functions

Dirac particle in electric field with confining scalar potential on (anti)-de Sitter background

2018 ◽  
Vol 33 (34) ◽  
pp. 1850202 ◽  
Author(s):  
N. Messai ◽  
B. Hamil ◽  
A. Hafdallah
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Electric Field ◽  
Scalar Potential ◽  
Dirac Particle ◽  
Wave Functions ◽  
De Sitter ◽  
Sitter Background ◽  
Position Representation

In this paper, we study the (1 + 1)-dimensional Dirac equation in the presence of electric field and scalar linear potentials on (anti)-de Sitter background. Using the position representation, the energy spectrum and the corresponding wave functions are exactly obtained.

Effects of barrier penetration on energy spectrum and wave functions in the path integral formalism

1978 ◽  
Vol 136 (2) ◽  
pp. 259-276 ◽  
Author(s):  
Iring Bender ◽  
Dieter Gromes ◽  
Heinz J. Rothe ◽  
Klaus D. Rothe
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Wave Functions ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Barrier Penetration

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.

scholarly journals DYNAMICAL SYMMETRY BREAKING IN THE EXTERNAL GRAVITATIONAL AND CONSTANT MAGNETIC FIELDS

1999 ◽  
Vol 14 (04) ◽  
pp. 481-503 ◽  
Author(s):  
T. INAGAKI ◽  
S. D. ODINTSOV ◽  
YU. I. SHIL'NOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Magnetic Fields ◽  
Symmetry Breaking ◽  
Effective Potential ◽  
Constant Magnetic Field ◽  
Dynamical Symmetry ◽  
Green Functions ◽  
Dynamical Symmetry Breaking ◽  
Njl Model

We investigate the effects of the external gravitational and constant magnetic fields to the dynamical symmetry breaking. As simple models of the dynamical symmetry breaking we consider the Nambu–Jona-Lasinio (NJL) model and the supersymmetric Nambu–Jona-Lasinio (SUSY NJL) model nonminimally interacting with the external gravitational field and minimally interacting with constant magnetic field. The explicit expressions for the scalar and spinor Green functions are found to the first order in the space–time curvature and exactly for a constant magnetic field. We obtain the effective potential of the above models from the Green functions in the magnetic field in curved space–time. Calculating the effective potential numerically with the varying curvature and/or magnetic fields we show the effects of the external gravitational and magnetic fields to the phase structure of the theories. In particular, increase of the curvature in the spontaneously broken phase of the chiral symmetry due to the fixed magnetic field makes this phase to be less broken. At the same time the strong magnetic field quickly induces chiral symmetry breaking even in the presence of fixed gravitational field within the nonbroken phase.

Path integral for spinning particle subjected to the constant electromagnetic field

2015 ◽  
Vol 30 (25) ◽  
pp. 1550124
Author(s):  
A. Merdaci ◽  
N. Boudiaf ◽  
L. Chetouani
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Transformation ◽  
Path Integral ◽  
Dirac Particle ◽  
Wave Functions ◽  
Integral Approach ◽  
Spinning Particle ◽  
Constant Electromagnetic Field ◽  
Special Cases ◽  
Electromagnetic Tensor

The problem of the Dirac particle submitted to a wave [Formula: see text] of a four-dimensional constant electromagnetic tensor is solved with the path integral approach via the use of Lorentz transformation and with an adequate choice for the velocity of the mobile referential.We show that the supersymmetric action associated to the pair [Formula: see text] can be determined from that associated to the pair [Formula: see text] and from that associated to the pair [Formula: see text] following simple relations.The wave functions and the energy spectrums are thus exactly determined and tested. Special cases are considered as well.

THE RELATIVISTIC LANDAU PROBLEM FOR FERMIONS

1992 ◽  
Vol 07 (29) ◽  
pp. 2731-2739
Author(s):  
J. GAMBOA
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Exact Expression ◽  
Integral Formalism ◽  
Planar Case ◽  
Spinning Particle ◽  
Relativistic Models ◽  
Popov Method

Using the Faddeev-Popov method an exact expression for the propagator of a relativistic spinning particle in a constant magnetic field is found. The conservation laws and the generators of the magnetic group are obtained in the path integral formalism. Both the relativistic and non-relativistic models are discussed in the planar case.

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