Abstract
We show that both in classical and quantum theory of the relativistic electron there are three sets of independent dynamical variables: position, velocity and momentum. The independence of velocity and momentum is interpreted by internal degrees of freedom. The geometry of the internal phase-space is discussed. The close analogy between the classical and quantum equations and their algebraic and symplectic structures is shown.
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References
For a simple derivation of this equation by analytic continuation and references to earlier papers see Barut, A.O., Phys. Rev. D10, 3335 (1974).
Wessel, W., Fortschritte der Physik 12, 409–440 (1964).
Barut, A.O. and Bracken, A.J., The Zitterbewegung and the Internal Geometry of the Electron, Phys. Rev. D (1981); Proc. Group Theory Conference, Lecture Notes in Physics, Vol. 135, p. 206–211 (Springer, 1980).
Schrödinger, E., Sitzungsb. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418 (1930).
Weyl, H., The Theory of Groups and Quantum Mechanics, (Dover, NY 1950), pp. 272–280.
Barut, A.O. and Bracken, A.J., Exact Solutions of Heisenberg Equations and Zitterbewegung of the Electron in a Constant Uniform Magnetic Field, Phys. Rev. D (to be published).
Barut, A.O. and Bracken A.J., The Magnetic Moment Operator of the Relativistic Electron (to be published).
In fact the radiative term in the Lorentz-Dirac equation (1) implies, in an external magnetic field, for example, a magnetic moment for the classical electron: Barut, A.O., Physics Letters 73B, 310 (1978).
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© 1982 Springer-Verlag Berlin Heidelberg
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Barut, A.O. (1982). What kind of a dynamical system is the radiating electron?. In: Doebner, HD., Andersson, S.I., Petry, H.R. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092429
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DOI: https://doi.org/10.1007/BFb0092429
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