Condensed Matter Physics, 2017, vol. 20, No. 1, 13002
DOI:10.5488/CMP.20.13002
arXiv:1704.02287
Title:
Helmholtz decomposition theorem and Blumenthal's extension by regularization
Author(s):

D. Petrascheck
(Institute for Theoretical Physics, University Linz, Altenbergerstr. 69, Linz, Austria)
,


R. Folk
(Institute for Theoretical Physics, University Linz, Altenbergerstr. 69, Linz, Austria)

Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is
possible for any asymptotically weakly decreasing vector field. He used a regularization method in his proof which can be extended to prove the theorem even for vector fields asymptotically increasing
sublinearly. Blumenthal's result is then applied to the timedependent fields of the dipole radiation and an artificial sublinearly increasing field.
Key words:
Helmholtz theorem, vector field, electromagnetic radiation
PACS:
01.30.mm, 03.50.De, 41.20.Jb
