Related papers: Coulomb Potential and Witten Superalgebra
Classes of relativistic symmetries accommodating supersymmetric patterns are considered for the Dirac Hamiltonian with axially-deformed scalar and vector potentials.
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries,…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
The hidden supersymmetry of the monopole found by De Jonghe et al. is generalized to a spin $\2$ particle in the combined field of a Dirac monopole plus a $\lambda^2/r^2$ potential [considered before by D'Hoker and Vinet], and related to…
The observation that the existance of the amazing reality and discreteness of the spectrum need not be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians.…
As is known, the so-called Dirac $K$-operator commutes with the Dirac Hamiltonian for arbitrary central potential $V(r)$. Therefore the spectrum is degenerate with respect to two signs of its eigenvalues. This degeneracy may be described by…
The theorem known from Pauli equation about operators that anticommute with Dirac's $K$-operator is generalized to the Dirac equation. By means of this theorem the operator is constructed which governs the hidden symmetry in relativistic…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $x{\rightarrow}\bar{x}^{\bar{\alpha}}$ has long been used as a method of simplifying spectral problems in quantum mechanics. This…
It is shown that for N=2 supersymmetry a hidden symmetry arises from the hybrid structure of a quartic algebra. The implications for invariant Lagrangians and multiplets are explored.
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
We analyze in detail the analytical solutions of the Dirac equation with scalar S and vector V Coulomb radial potentials near the limit of spin and pseudospin symmetries, i.e., when those potentials have the same magnitude and either the…
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…
We investigate a new realization of extended quantum-mechanical supersymmetry. We first show that an $\mathcal{N}=2$ quantum-mechanical supersymmetry is hidden in the four-dimensional (4D) spectrum of the Kaluza-Klein decomposition for the…
We show that the N=2 superextended 1D quantum Dirac delta potential problem is characterized by the hidden nonlinear $su(2|2)$ superunitary symmetry. The unexpected feature of this simple supersymmetric system is that it admits three…