相关论文: Localizing the Relativistic Electron

We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead to a structure very similar to the…

Different operators have been suggested in the literature to describe the electron's spin degree of freedom within the relativistic Dirac theory. We compare concrete predictions of the various proposed relativistic spin operators in…

Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…

We extract the square root of the Minkowski metric using Dirac/Clifford matrices. The resulting $4\times 4$ operator $d{\bf S}$ that represents the square root, can be used to transform four vectors between relatively moving observers. This…

The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…

The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativity. Recent work of Chamseddine and Connes suggests that…

This article compares treatments of the Stern-Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a…

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…

The causality issues concerning the localization of relativistic quantum systems, as evidenced by Hegerfeld's paradox, are addressed through a proper-time formalism of single-particle operators. Starting from the premise that physical…

The problem of Dirac's equation in a rotating electromagnetic field can be reduced to the stationary by using a transformation for point rotating reference frames. The general form of the non-Galilean transformation is deduced in the paper.…

The electron, which has been pictured as an elementary particle ever since J.J. Thomson's e/m-measurement in 1897, and the relativistic motion of which is described by the Dirac equation, is discussed in the light of the recent progress…

Localization of relativistic particles and their position-momentum uncertainty relations are not yet fully understood. We discuss two schemes of photon localization that are based on the energy density. One scheme produces a positive…

A novel interpretation is given of Dirac's "wave equation for the relativistic electron" as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different "topological spin"…

The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…

We prove spectral and dynamical localization for a one-dimensional Dirac operator to which is added an ergodic random potential, with a discussion on the different types of potential. We use scattering properties to prove the positivity of…

In the realm of relativistic quantum mechanics, we address a fundamental question: Which one, between the Dirac or the Foldy-Wouthuysen density, accurately provide a probability density for finding a massive particle with spin $1/2$ at a…

We have studied a relativistically covariant Stern-Gerlach (SG) experiment for a relativistic spin and a Dirac spin. We have obtained the relativistic spin in an arbitrary frame by using the classical spin dipole tensor, which gives the…

A field-theoretical space-time position operator can be properly introduced for the Dirac field, it plays the role of a generalized Noether charge associated with a local symmetry, and its second-quantized form shows that quantum fields…

We use the Foldy--Wouthuysen (unitary) transformation to give an alternative characterization of the eigenvalues and eigenfunctions for the Brown-Ravenhall operator (the projected Dirac operator) in the case of a one-electron atom. In…

We demonstrate, by solving numerically the time-dependent Schroedinger equation, the physical character of electron localization in a disordered two-dimensional lattice. We show, in agreement with the prediction of P. W. Anderson, that the…