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[en] The radiation reaction force and equations of motion for Barut's modified action, which is the classical model of the electron exhibiting zitterbewegung, were obtained and this equation reduces to the Lorentz-Dirac equation in the spinless limit

[en] A generalized continuity equation extending the ordinary continuity equation is found using quanternions to show it is compatible with Dirac, Schrödinger, Klein–Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by the Schrödinger-like equation and not by the diffusion equation. (fundamental areas of phenomenology (including applications))

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[en] This article presents a simple way of consistently incorporating two new field variables to the set of Maxwell-like equations: the Lagrangian density of the system is written in terms of eight field variables, from which the equations of motion are obtained. The quantized version of the corresponding free-field theory is also briefly discussed

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[en] A free particle is constrained to move on a knot obtained by winding around a putative torus. The classical equations of motion for this system are solved in a closed form. The exact energy eigenspectrum, in the thin torus limit, is obtained by mapping the time-independent Schrödinger equation to the Mathieu equation. In the general case, the eigenvalue problem is described by the Hill equation. Finite-thickness corrections are incorporated perturbatively by truncating the Hill equation. Comparisons and contrasts between this problem and the well-studied problem of a particle on a circle (planar rigid rotor) are performed throughout

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[en] We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schroedinger equation to illustrate the methodology. Stationary solutions to the discrete time Schroedinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein-Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantization of discrete time mechanics and discrete time quantum electrodynamics. (author)