Dirac Derivatives Research Articles

Radiation reaction in classical electrodynamics

The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In particular, almost all solutions are dynamically unstable, and therefore, highly questionable. The question remains whether better equations of motion than LAD can be found to describe the dynamics of charges in the electromagnetic fields. In this paper we present an approach to derive such equations of motions, taking as input the Maxwell equations and a particular charge model only, similar to the model suggested by Dirac in his original derivation of LAD in 1938. We present a candidate for new equations of motion for the case of a single charge. Our approach is motivated by the observation that Dirac's derivation relies on an unjustified application of Stokes' theorem and an equally unjustified Taylor expansion of terms in his evolution equations. For this purpose, Dirac's calculation is repeated using an extended charge model that does allow for the application of Stokes' theorem and enables us to find an explicit equation of motion by adapting Parrott's derivation, thus avoiding a Taylor expansion. The result are second order differential delay equations, which describe the radiation reaction force for the charge model at hand. Their informal Taylor expansion in the radius of the charge model used in the paper reveals again the famous triple dot term of LAD but provokes the mentioned dynamical instability by a mechanism we discuss and, as the derived equations of motion are explicit, is unnecessary.

A Matter of Principle: The Principles of Quantum Theory, Dirac’s Equation, and Quantum Information

This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation for the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall, however, also consider Heisenberg's derivation of quantum mechanics, which inspired Dirac. I argue that Heisenberg's and Dirac's work alike was guided by their adherence to and confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by G. M. D' Ariano and his coworkers on the principles of quantum information theory, which extends quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equation from these principles alone, without using the principles of relativity.

Dirac's equation and the nature of quantum field theory

This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.

On the derivation of zitterbewegung

Abstract We show how we can remove the inconsistencies recently pointed out by Sherry in regard to Dirac's derivation of zitterbewegung.