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Relativistic dynamics of a spinning magnetic particle

Published online by Cambridge University Press:  24 October 2008

Myron Mathisson
Myron Mathisson
Affiliation:
Communicated by P. A. M. Dirac
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Extract

The author's general variational method is applied to the case of a particle for which second moments are important but third and higher moments are negligible. Equations of motion are obtained for the angular momentum and for the centre of mass, equations (12·35) and (12·41), with arbitrary external forces X.

The angular forces are then calculated for a charged particle with electric and magnetic moments moving in a general electromagnetic field, on the assumption that the effect of a certain part of the energy tensor, Tiii of (15·17), is negligible. This leads to the equations of angular motion, (17·13), from which it is inferred that, in order that the magnitude of the angular momentum may be integrable, the angular momentum, electric and magnetic moments must all be parallel in a frame of reference in which the particle is instantaneously at rest.

The linear forces are then calculated for the case of no electric moment, leading to the equations for linear motion (18·10). From these it is inferred that, in order that the mass may be integrable, the ratio of the magnetic moment to the angular momentum must be constant.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 1 , January 1942 , pp. 40 - 60
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

‡ The following misprints have been noted. The integrands of (8·8) and (8·13) should be divided by n λn λ. Equation (8·14) should read and (10·16) should read The final results in each case (e.g. (8·17) and (8·18)) are correct.

† We omit the limits of integration.

† From (12·16) and (13·7), we have m′ikδ + m′kid = 0. The limitation involved can be conveniently interpreted in terms of a classical rigid body when we state that the ellipsoid of inertia of the physical system considered reduces to a sphere. [Mathisson, M., Acta Phys. Polonica, 6 (1937), 186.]Google Scholar