DocumentCode :
791589
Title :
Electromagnetic quantities in 4-D space and the dual Hodge operator
Author :
Fournet, G.
Author_Institution :
Lab. de Genie Electrique, Univ. de Paris VI et XI, Gif-sur-Yvette, France
Volume :
149
Issue :
4
fYear :
2002
fDate :
7/1/2002 12:00:00 AM
Firstpage :
158
Lastpage :
164
Abstract :
Two aspects of the presentation of electromagnetism in three-dimensional space can be compared if a distinction is made between polar vectors P and axial vectors T. In option α, Baldomir and Hammond take B, E, , , as basic vectors and need to use the *Hodge dual operator. Option β is presented based on the vectors B, E, , , where no special operator is required. For the presentation of electromagnetism in four-dimensional space the components of the group E B, common to both options, are brought together to form a tensor of 42 = 16 components. The Bij are arranged within a 3 × 3 square, with the E k on the edge of this square. The slightly different forms of this arrangement correspond to the tensors identified symbolically by F pq (B, E) for option α and F km (B, E) for option β. Two Maxwell equations are related to the corresponding tensors for each option. For option β, a tensor Gkm directly linked to F km (B, E) naturally leads to and . The consideration of this tensor along with the four-dimensional current density vector Jβ (expressed using and ρ) allows one to establish the two other Maxwell equations
Keywords :
Maxwell equations; current density; tensors; vectors; 4D space; Maxwell equations; axial vectors; current density vector; dual Hodge operator; electromagnetic quantities; electromagnetism; polar vectors; tensor;
fLanguage :
English
Journal_Title :
Science, Measurement and Technology, IEE Proceedings -
Publisher :
iet
ISSN :
1350-2344
Type :
jour
DOI :
10.1049/ip-smt:20020406
Filename :
1020877
Link To Document :
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