Spin Two-Body Problem of Classical Electrodynamics with Radiation Terms (I) – Derivation of Spin Equations (original) (raw)
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Results in nonlinear analysis, 2021
In the present paper spin equations for three-body problem of classical electrodynamics are introduced. They should be considered jointly with 3-body equations of motion derived in a previous paper of the author. The system of spin equations is an overdetermined one. It is shown that the independent spin equations are nine in number as many as the components of the unknown spin functions. The system obtained will be solved by the xed-point method in a next paper.
Two-Body Problem of Classical Electrodynamics with Radiation Terms-Derivation of Equations (I)
International Journal of Theoretical and Mathematical Physics, 2015
This paper is the first part of our investigations devoted to the two-body problem of classical electrodynamics. The primary purpose of this first part is to derive equations of motion describing two moving charged mass particles taking into account the radiation. We proceed from the suggestions given by J. L. Synge [1]. He has proposed a formulation of the of relativistic two-body problem with usually accepted Dirac’s radiation terms [2] containing second derivatives of the velocities: , Here we propose a general approach to introduce new equations of motion based on the same Dirac’s physical assumptions from [2]. Instead of the above system of eight equations of motion we derive consider an analogous system , where the classical Lorentz-Dirac radiation terms are replaced by newly derived ones. We show that two equations are consequences of the rest ones and so we have to solve a system of six equations for six unknown velocities, issue that has not been discussed in the literature...
Equation of motion in classical electrodynamics. II
Physical Review D, 1980
With the aid of the principle of equivalence, we extend our development of an equation of motion for a radiating charged particle to include movement in both a gravitational and an electromagnetic field. The rate of electromagnetic radiation is given by the covariant generalization of the Larmor formula for flat space-time. The proposed equation of motion exhibits none of the difficulties that are associated with the covariant extension of the Lorentz-Dirac equation. We apply our results to the simple examples of a charged particle falling in a gravitational field and a charged particle held fixed in a quasiuniform gravitational field. '~e f. 4, p. 106. 'OD.
Advances in Applied Clifford Algebras, 2017
Using Clifford and Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to Dirac-Hestenes equation satisfied by a class of spinor fields that we call classical spinor fields. These spinor fields are characterized by having the Takabayashi angle function constant (equal to 0 or π). We also investigate a nonlinear Dirac-Hestenes like equation that comes from a class of generalized classical spinor fields. Finally, we show that a general Dirac-Hestenes equation (which is a representative in the Clifford bundle of the usual Dirac equation) gives a generalized Hamilton-Jacobi equation where the quantum potential satisfies a severe constraint and the "mass of the particle" becomes a variable. Our results can then eventually explain experimental discrepancies found between prediction for the de Broglie-Bohm theory and recent experiments. We briefly discuss de Broglie's double solution theory in view of our results showing that it can be realized, at least in the case of spinning free particles.The paper contains several Appendices where notation and proofs of some results of the text are presented.
On a General Spin Dirac Equation
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In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). We believe that the fact that this modification is consistent with the STR gives the present effort some physical justification that warrants further investigations. From the vantage point of unity, simplicity and beauty, it is natural to wonder why should there exist different equations to describe particles of different spins? For example, the Klein-Gordon equation describes spin-0 particles, while the Dirac Equation describes spin-1/2, and the Rarita-Schwinger Equation describes spin-3/2. Does it mean we have to look for another equation to describe spin-2 particles, and then spin-5/2 particles etc? This does not look beautiful, simple, or at the very least suggest a Unification of the Natural Laws. Beauty of a theory is not a physical principle but, one thing is clear to the searching mind-i.e., a theory that possesses beauty, appeals to the mind, and is (posteriori) bound to have something to do with physical reality if it naturally submits itself to the test of experience. The effort of the present reading is to make the attempt to find this equation.
Electromagnetic fields in relativistic one-particle equations
Chemical Physics, 2009
In this work we reconsider magnetic-field operators in Dirac-based one-electron equations and their behaviour under unitary transformations. When approaching the non-relativistic limit within a fourcomponent theory, the emergence of the diamagnetic contribution to second-order properties needs to be explained. This then requires to show how the magnetic-field-dependent terms that are all linear in the vector potential arrange to yield the quadratic (bilinear) term, which is the so-called diamagnetic term. An interesting suggestion by Kutzelnigg solves this problem on the operator level by invoking a unitary transformation of the electromagnetic-field-containing one-electron Dirac Hamiltonian. Naturally, this suggestion leads to the more general question of whether the vector potential needs to be incorporated into the unitary transformation that is used in transformation techniques for a decoupling of positive-and negative-energy states. We examine all different possibilities of how to transform the vector-potential-containing Dirac Hamiltonian from the perspective of the most general parametrization of unitary matrices with a special focus on the final goal to employ them in perturbative treatments of molecular property calculations. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c h e m p h y s
Advances in Mathematical Physics
We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coo...
In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). From the vantage point of unity, simplicity and beauty, it is natural to wonder why should there exist different equations to describe particles of different spins? For example, the Klein-Gordon equation describes spin-0 particles, while the Dirac Equation describes spin-1/2, and the Rarita-Schwinger Equation describes spin-3/2. Does it mean we have to look for another equation to describe spin-2 particles, and then spin-5/2 particles etc? This does not look beautiful, simple, or at the very least suggest a Unification of the Natural Laws.
The European Physical Journal Plus, 2011
An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the selffield generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self 4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed respectively in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.