Electromagnetic fields and potentials generated by massless charged particles

Journal Article · Wed Oct 15 04:00:00 EDT 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.06.005· OSTI ID:22403398

Azzurli, Francesco ^[1]; Lechner, Kurt ^[2]

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1. Scuola Galileiana di Studi Superiori, Università degli Studi di Padova (Italy)
2. Dipartimento di Fisica e Astronomia, Università degli Studi di Padova (Italy)

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates a planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.

• OSTI ID: 22403398
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 349; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHARGED PARTICLES
DELTA FUNCTION
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
EXACT SOLUTIONS
MASSLESS PARTICLES
MAXWELL EQUATIONS
POTENTIALS
SHOCK WAVES
SINGULARITY
VISIBLE RADIATION