DISSIPATIVE POTENTIALS AND THE MOTION OF A CLASSICAL CHARGE. PART II

Journal Article · Fri Nov 01 04:00:00 EST 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.132.1321· OSTI ID:4628020

Leaf, B

Examples of the motion of a point charge were found to be consistent with the hypothesis of Abraham that the mass of an electron (or positron) is entirely electromagnetic. Further consequences of this hypothesis are developed. It is shown that the conservation laws of the electromagnetic field and Maxwell's equations require that the total Lorentz force (including the self-force) on the charge should vanish. This result can be expressed as a Lagrangian equation of motion. The canonical four momentum of the charge is the product of the magnitude of the charge by the four potential of the field at the position of the charge. When the dissipative form of the potertial for an unconfined point charge is used, the integro-differential equation of motion is obtained for a particle with zero bare mass. A mechanical rnornentum and mass are defined; these are associated with the singular part of the Green's function for the D'Alembert equation. The rate of change of this mechanical momentum is equal to the sum of the external force, the radiation damping force (with the correct sign obtained by the use of the retarded fields), and the gradient at the position of the charge of its Coulombic self-potential energy. For a particle assumed to follow a continuous trajectory, the integrals in the integro-differential equation of motion are evaluated by a procedure in agreernent with, but much simpler than, that of Dirac. The result is the unrenormalized equation of Dirac for a particle whose mass is the divergent Coulombic self-energy. The effective rnomenturn and mass in this equation are reduced to half of the mechanical momentum and mass by the force term arising from the gradient of the Coulombic self-potential energy. (auth)

• Research Organization: Kansas State Univ., Manhattan
• NSA Number: NSA-17-041627
• OSTI ID: 4628020
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 132; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
ELECTRIC CHARGES
ELECTRIC FIELDS
ELECTRIC POTENTIAL
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
ELECTRONS
ENERGY
GREEN FUNCTION
INTERACTIONS
LAGRANGIAN
LORENTZ FORCE
LOSSES
MAGNETIC FIELDS
MASS
MOMENTUM
MOTION
PARTICLE MODELS
PHYSICS
POSITRONS
RADIATIONS
VELOCITY