Related papers: Relativistic Quantum Dynamics on a Double Cone
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
A detailed study of the classical and quantum mechanics of a free particle on a double cone and the particle bounded to its tip by the harmonic oscillator potential is presented.
We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic…
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic…
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum…
General relativistic quantum dynamics of twisted (vortex) Dirac particles is constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived for a twisted relativistic electron in arbitrary electric…
A (globally) neutral two-body system is supposed to obey a pair of coupled Klein-Gordon equations in a constant homogeneous magnetic field. Considering eigenstates of the pseudomomentum four-vector, we reduce these equations to a…
The relativistic two body problem is considered in terms of the action integral in the case of two interacting spinless particles and spin-$1/2$ fermions, interacting by means of vector and scalar fields. The Lagrangians governing the…
This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
The spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background built from two Dirac delta potentials is studied. A distinction will be made between mass-spike and…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
The Dirac equation in a chromomagnetic field is solved for colored particle moving in a limited space volume. Quantized energy levels and the corresponding wave functions are found for backgrounds both directed along third axes and having…
We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a…
Local symmetries of the action for a relativistic particle with curvature and torsion of its world curve in the (2+1)-dimensional space-time are studied. With the help of the method, worked out recently by the authors (Phys.Rev., D56, 1135,…
We investigate torsion and noninertial effects on a spin-$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference…