Relativistic classical theory of a free particle

Journal Article · Fri Aug 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532077· OSTI ID:526887

Bosanac, S D ^[1]

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1. R. Boskovic Institute, 10001 Zagreb, Republic of (Croatia)

By shifting the emphasis from the concept of trajectory to the concept of probability density it is possible to incorporate the uncertainty principle into classical mechanics. This amendment in the nonrelativistic classical theory is sufficient to derive the Schr{umlt o}dinger equation for a general potential. In order to show that the approach has general validity it is necessary to show that it can be generalized to the classical relativistic dynamics. In this paper it is shown how this generalization is achieved for a free particle, and as a result the Dirac instead of the Klein{endash}Gordon equation is obtained. It is shown that the spin and the magnetic moment of charged particles are classical in character because their correct values are calculated as the averages over the classical (relativistic) phase space density, subject to the constraint imposed by the uncertainty principle. Since the Dirac equation has direct connection to the classical (relativistic) dynamics the problem of the positive and negative energy states is discussed. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 526887
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHARGED PARTICLES
CLASSICAL MECHANICS
DIRAC EQUATION
ENERGY
KLEIN-GORDON EQUATION
MAGNETIC MOMENTS
PROBABILITY
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
SPIN
TRAJECTORIES
UNCERTAINTY PRINCIPLE