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Electromagnetism in Space-Time

In: Directed Quantities in Electrodynamics

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  • Bernard Jancewicz

    (University of Wrocław, Institute of Theoretical Physics)

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.

Suggested Citation

  • Bernard Jancewicz, 2021. "Electromagnetism in Space-Time," Springer Books, in: Directed Quantities in Electrodynamics, chapter 0, pages 265-316, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-90471-5_7
    DOI: 10.1007/978-3-030-90471-5_7
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