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We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac-Coulomb and the…
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…
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 discuss some aspects of the gravitational interaction of the relativistic quantum particles with spin 1/2. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. The…
The exact Foldy-Wouthuysen transformation is performed in order to study the Dirac field interacting with many possible external fields associated with CPT-Lorentz violation. We also derived the calculation of equations of motion as well as…
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…
A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller…
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…
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…
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…
We apply the method of direct perturbation theory for the Foldy-Wouthuysen (FW) transformation upon the Dirac-Pauli Hamiltonian subject to external electromagnetic fields. The exact FW transformations exist and agree with those obtained by…
The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask…
The Thomas-Bargmann-Michel-Telegdi (T-BMT) equation is derived using the Exact Foldy-Wouthuysen transformation. Extra new terms were found, and we discuss their possible physical applications. The main point of this work is to detail the…
Recent interest in the studies of structured states obtained in relativistic electron beams has highlighted the use of two alternative descriptions, each based on a different wavefunction and the related space-time density. Although both…
Goncalves et al. derived a non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using the exact Foldy-Wouthuysen transformation. This gave rise to the intriguing notion that spin-precession…
A general method of the Foldy-Wouthyusen (FW) transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite…
Based on an extension of the Foldy--Wouthuysen method to two-body equations, the problem of expansion of equal-time relativistic equations for two Dirac particles in powers of $1/c$ to higher orders is considered. For the case of two…
The classical dynamics for a charged spin particle is governed by the Lorentz force equation for orbital motion and by the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation for spin precession. In static and homogeneous electromagnetic…
In this work we analyze the low energy nonrelativistic limit of Dirac theory in the framework of effective field theory. By integrating out the high energy modes of Dirac field, given in terms of a combination of the two-components Weyl…
It has long been speculated that the Dirac or, more generally, the Dirac-Pauli spinor in the Foldy-Wouthuysen (FW) representation should behave like a classical relativistic spinor in the low-energy limit when the probability of…