Degeneracy and Para-supersymmetry of Dirac Hamiltonian in (2+1)- Spacetime

The quantum mechanics of a spin 1/2 particle on a locally spatial constant curvature part of a (2+1)- spacetime in the presence of a constant magnetic field of a magnetic monopole has been investigated. It has been shown that these 2-dimensional Hamiltonians have the degeneracy group of SL(2,c), and para-supersymmetry of arbitrary order or shape invariance. Using this symmetry we have obtained its spectrum algebraically. The Dirac's quantization condition has been obtained from the representation theory. Also, it is shown that the presence of angular deficit suppresses both the degeneracy and shape invariance.Comment: 31 pages, Latex, no figures, to be published in J. Math. Phy

Formulation of Electrodynamics with an External Source in the Presence of a Minimal Measurable Length

In a series of papers, Quesne and Tkachuk (J. Phys. A: Math. Gen. \textbf{39}, 10909 (2006); Czech. J. Phys. \textbf{56}, 1269 (2006)) presented a $D+1$-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal measurable length. In this paper, the Lagrangian formulation of electrodynamics in a 3+1-dimensional space-time described by Quesne-Tkachuk algebra is studied in the special case $\beta'=2\beta$ up to first order over the deformation parameter $\beta$. It is demonstrated that at the classical level there is a similarity between electrodynamics in the presence of a minimal measurable length (generalized electrodynamics) and Lee-Wick electrodynamics. We obtain the free space solutions of the inhomogeneous Maxwell's equations in the presence of a minimal length. These solutions describe two vector particles (a massless vector particle and a massive vector particle). We estimate two different upper bounds on the isotropic minimal length. The first upper bound is near to the electroweak length scale $(\ell_{electroweak}\sim 10^{-18}\, m)$, while the second one is near to the length scale for the strong interactions $(\ell_{strong}\sim 10^{-15}\, m)$. The relationship between the Gaete-Spallucci nonlocal electrodynamics (J. Phys. A: Math. Theor. \textbf{45}, 065401 (2012)) and electrodynamics with a minimal length is investigated.Comment: 13 pages, no figur

Exact solutions of Dirac equation on (1+1)-dimensional spacetime coupled to a static scalar field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.Comment: 7 pages, Late

Formulation of an Electrostatic Field with a Charge Density in the Presence of a Minimal Length Based on the Kempf Algebra

In a series of papers, Kempf and co-workers (J. Phys. A: Math. Gen. {\bf 30}, 2093, (1997); Phys. Rev. D {\bf52}, 1108, (1995); Phys. Rev. D {\bf55}, 7909, (1997)) introduced a D-dimensional $(\beta,\beta')$-two-parameter deformed Heisenberg algebra which leads to a nonzero minimal observable length. In this work, the Lagrangian formulation of an electrostatic field in three spatial dimensions described by Kempf algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that there is a similarity between electrostatics in the presence of a minimal length (modified electrostatics) and higher derivative Podolsky's electrostatics. The important property of this modified electrostatics is that the classical self-energy of a point charge becomes a finite value. Two different upper bounds on the isotropic minimal length of this modified electrostatics are estimated. The first upper bound will be found by treating the modified electrostatics as a classical electromagnetic system, while the second one will be estimated by considering the modified electrostatics as a quantum field theoretic model. It should be noted that the quantum upper bound on the isotropic minimal length in this paper is near to the electroweak length scale $(\ell_{electroweak}\sim 10^{-18}\, m)$.Comment: 11 pages, no figur

Families of exact solutions of a 2D gravity model minimally coupled to electrodynamics

Three families of exact solutions for 2-dimensional gravity minimally coupled to electrodynamics are obtained in the context of ${\cal R}=T$ theory. It is shown, by supersymmetric formalism of quantum mechanics, that the quantum dynamics of a neutral bosonic particle on static backgrounds with both varying curvature and electric field is exactly solvable.Comment: 13 pages, LaTeX, to be published in JM

Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. {\bf 39}, 10909, 2006) introduced a (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$. Applying the condition $\beta<\frac{1}{8m^{2}c^{2}}$ to an electron, the upper bound for the isotropic minimal length becomes about $3 \times 10^{-13}m$. This value is near to the reduced Compton wavelength of the electron $(\lambda_c = \frac{\hbar}{m_{e}c} = 3.86\times 10^{-13} m)$ and is not incompatible with the results obtained for the minimal length in previous investigations.Comment: 11 pages, no figur