General classical theory of spinning particles in a meson field

An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant χ =μ /hslash of the dimensions of a reciprocal length, μ being the meson mass, and as χ → 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88 a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 109 eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p4/E2 (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E ~ 3\cdot 5μ , its value at this point being 3 × 10-26 cm.2, after which it decreases rapidly, becoming proportional to E-2 at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E gtrsim 3μ . The scattering of longitudinally polarized mesons is due to the translational but not the rotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and - e may occur in nature, the above results can be applied to charged mesons. Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3\cdot 5μ . Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3μ . Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes

Classical theory of mesons

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On the theory of point-particles

It is deduced from the conservation of the energy-momentum tensor that if the flow of energy and momentum into a tube surrounding a time-like world-line, on which the field is singular, become singular as the size of the tube is contracted to zero, then the singular terms are necessarily perfect differentials of quantities on the world-line with respect to the proper time along the world-line. The same can be proved of any other tensor, as, for example, the angular-momentum tensor, which is conserved. It is proved from this that for any point-particle whatever having charge, spin or other properties, which need not be specified, it is always possible to deduce exact equations of motion which are finite. It is proved further that if the energy-momentum tensor is altered by the addition of partial Kμ ν σ/partial xσ, where Kμ ν σ is any tensor antisymmetric in ν and σ , then the equations of motion are unaltered, but it is possible to choose Kμ ν σ in such a way as to make the flow of energy and momentum into a given tube non-singular

Radiation from a Charge Uniformly Accelerated for All Time

A recent paper of Singal [Gen. Rel. Grav. 27 (1995), 953-967] argues that a uniformly accelerated particle does not radiate, in contradiction to the consensus of the research literature over the past 30 years. This note points out some questionable aspects of Singal's argument and shows how similar calculations can lead to the opposite conclusion.Comment: LaTeX, 9 pages, to appear in General Relativity and Gravitatio

Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics

The usual action integral of classical electrodynamics is derived starting from Lanczos's electrodynamics -- a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell's equations interpreted as a generalization of the Cauchy-Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell's equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction so that the mass is finite, and that the only approximation made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical "bag" confining the quarks in a hadron, so that Lanczos's electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles.Comment: 16 pages. Final version to be published in "Foundations of Physics

Relativistic wave equations for the proton

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Classical theory of electrons

It is shown that when a point charge is present in an electromagnetic field, the conservation of energy and momentum does not in general lead to conservation of angular momentum for the system as a whole. The conservation laws impose stringent restrictions on the possible equations which may describe the motion of the point charge.If it is required that higher derivatives of the velocity than the second should not appear explicitly in these equations, then the choice is unique and the only possible equations are those originally derived by Lorentz. If the third derivative is allowed to appear explicitly in the equations, but no thigher ones, then it is possible to give one other system of equations for describing the behaviour of a point singularity which can be used without entirely artificial initial and final conditions

The algebraic hyperstructure of elementary particles in physical theory

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.Comment: 13 page

Classical theory of spinning particles

The exact relativistic classical equations taking radiation reaction into account for the rotation and translation of apoint dipole are given for the case where the dipole is always a pure magnetic dipole in the rest system. These equations are entirely free from any singularities. It is shown that the mass M, angular momentum of the spin I and magnetic moment g2 are three entirely independent constants with no connection between them. The cross-section for the scattering of light by a dipole is given by formula (56). This formula shows that due to radiation reaction the scattering actually decreases as ω-2 for very high frequencies ω, instead of increasing as ω2 when radiation reaction is neglected. The quantum mechanical formula for the scattering of neutral mesons by neutrons is shown to go wrong at energies h ω ≥ 3 μ due to neglect of the effects of radiation damping. The classical formula (56) can still be correctly applied in the range 3μ <h ω < M, where the quantum formula is wrong, M being the neutron mass. Finally reasons are given for thinking that the quantum theory of the electron fails at energies above about √3 × 137m due to neglect of the effect of radiation damping on the spin, and the quantum theory of the meson and its inter-action with the electromagnetic field at √6 × 137µ