相关论文: Analytic Representation of The Dirac Equation
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…
The low-energy and weak-field limit of Dirac equation can be obtained by an order-by-order block diagonalization approach to any desired order in the parameter $\pi/mc$ ($\pi$ is the kinetic momentum and $m$ is the mass of the particle). In…
This paper offers educational insight into the Dirac equation, examining its historical context and contrasting it with the earlier Schr\"odinger and Klein-Gordon (KG) equations. The comparison highlights their Lorentz transformation…
We investigate the nonrelativistic limit of the gravitationally coupled Dirac Equation via a Foldy-Wouthuysen transformation. The relativistic correction terms have immediate and obvious physical interpretations in terms of a gravitational…
The Foldy-Wouthuysen transformation of the Dirac Hamiltonian is generally taught as simply a mathematical trick that allows one to obtain a two-component theory in the low-energy limit. It is not often emphasized that the transformed…
Non-localities of Foldy-Wouthuysen and related transformations, which are used to separate positive and negative energy states in the Dirac equation, are investigated. Second moments of functional kernels generated by the transformations…
The worldline of a free electron is revealed by applying Dirac's velocity operator to its Dirac wave function whose space-time arguments are expressed in a proper time by a Lorentz transformation. This motion can be decomposed into two…
The semiclassical limit for Dirac particles interacting with a static gravitational field is investigated. A Foldy-Wouthuysen transformation which diagonalizes at the semiclassical order the Dirac equation for an arbitrary static spacetime…
This paper presents a relativistic symmetrical interpretation of the Dirac equation in 1+1 dimensions which predicts no zitterbewegung for a free spin-1/2 particle. This could resolve the longstanding puzzle of zitterbewegung in…
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…
We present a classical optics simulation of the one-dimensional Dirac equation for a free particle. Positive and negative energy components are represented by orthogonal polarizations of a free propagating beam, while the spatial profile…
The purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of…
Inspired by the reconstituted similarity renormalization group method, the reconstituted Foldy-Wouthuysen (FW) transformation is proposed. Applied to the Dirac equation in the covariant density functional theory, the reconstituted FW…
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn…
This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. It has recently been shown that, despite the addition of…
We show that the origin of the nonequivalence of Hamiltonians in different representations is a change of the form of the time-derivative operator at a time-dependent unitary transformation. This nonequivalence does not lead to an ambiguity…
We carry out a direct, iterative Foldy--Wouthuysen transformation of a general Dirac Hamiltonian coupled to an electromagnetic field, including the anomalous magnetic moment. The transformation is carried out through an iterative…
We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordstrom…
The block-diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proved.…
For Dirac particles interacting with external fields, we use the exact operator of the Foldy-Wouthuysen transformation obtained by Eriksen and rigorously derive a leading correction in the weak-field approximation to the known relativistic…