Related papers: The Relativistic Dirac-Morse Problem via SUSY QM
This paper describes a tentative relativistic quantum mechanics approach inspired by Dirac's point-form, which is based on the physics description on a hyperboloid surface. It is mainly characterized by a non-standard relation of the…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…
Solutions to a scalar-tensor (dilaton) quantum gravity theory, interacting with quantized matter, are described. Dirac quantization is frustrated by quantal anomalies in the constraint algebra. Progress is made only after the…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation, write the first and second-order equations from it, and then we solve…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
I discuss the role of relativistic quantum mechanics in few-body physics, various formulations of relativistic few-body quantum mechanics and how they are related.
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves…
In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from…
We propose a numerical method of estimating various physical quantities in lattice (supersymmetric) quantum mechanics. The method consists only of deterministic processes such as computing a product of transfer matrix, and has no…
We discuss a new realization of $\mathcal{N}$-extended quantum-mechanical supersymmetry (QM SUSY) with central charges hidden in the four-dimensional (4D) mass spectrum of higher dimensional Dirac action with curved extra dimensions. We…
We study one dimensional supersymmetric (SUSY) quantum mechanics of a spin 1/2 particle moving in a rotating magnetic field and scalar potential. We also discuss SUSY breaking and it is shown that SUSY breaking essentially depends on the…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the…
We consider deformed special relativity (DSR) theories on commutative space-time, perhaps as an first approximation to a noncommutative space-time formulation. The corresponding field theories in general possess derivatives of all orders.…
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of…