Helmholtz theorem for antisymmetric second‐rank tensor fields and electromagnetism with magnetic monopoles
作者:
Donald H. Kobe,
期刊:
American Journal of Physics
(AIP Available online 1984)
卷期:
Volume 52,
issue 4
页码: 354-358
ISSN:0002-9505
年代: 1984
DOI:10.1119/1.13668
出版商: American Association of Physics Teachers
关键词: magnetic monopoles;space−time;electromagnetism;tensor fields;helmholtz theorem;current density;maxwell equations
数据来源: AIP
摘要:
A generalized Helmholtz’s theorem is proved, which states that an antisymmetric second‐rank tensor field in 3+1 dimensional space‐time, which vanishes at spatial infinity, is determined by its divergence and the divergence of its dual. When the divergence of the antisymmetric electromagnetic field strength tensor is equal to the electric charge‐current density and the divergence of the dual of the electromagnetic field strength tensor is equal to the magnetic charge‐current density, the equations of electromagnetism are obtained. As a convenience, in the solution of the equations of electromagnetism two different four‐vector potentials can be used, one of which couples to the electric charge‐current density and the other to the magnetic charge‐current density.
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