Electromagnetism in Space-Time

Bernard Jancewicz
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Bernard Jancewicz: University of Wrocław, Institute of Theoretical Physics

Chapter Chapter 7 in Directed Quantities in Electrodynamics, 2021, pp 265-316 from Springer

Abstract: Abstract This chapter is devoted to considerations in four-dimensional space-time. It starts in Sect. 7.1 with a description of directed quantities in a four-dimensional vector space. The transition from three-dimensional space to a plane described in a previous chapter is helpful to perform the passage in opposite direction, namely from three to four dimensions, in Sect. 7.2. A distinguished vector protruding in the fourth dimension is necessary for this—its direction determines time axis. In space-time, two field quantities, namely a Faraday two-form F joining the B and E fields, and a Gauss two-from uniting the D and H fields, are sufficient to write down two of Maxwell’s equations with the use of exterior derivatives of differential forms. They are independent of the metric of space-time.

Date: 2021
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DOI: 10.1007/978-3-030-90471-5_7

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