Generalized Maxwell equations for exterior-algebra multivectors in (k, n) space-time dimensions
| Autor: | Alfonso Martinez, Josep Font-Segura, Ivano Colombaro |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Electromagnetic field
Pure mathematics Stress-energy tensor Multivectors Rank (linear algebra) Differential form General Physics and Astronomy FOS: Physical sciences Mathematical Physics (math-ph) Exterior calculus symbols.namesake Maxwell's equations Maxwell equations symbols Tensor Exterior algebra Lorentz force Vector calculus Mathematical Physics Mathematics |
| Popis: | This paper presents an exterior-algebra generalization of electromagnetic fields and source currents as multivectors of grades $r$ and $r-1$ respectively in a flat space-time with $n$ space and $k$ time dimensions. Formulas for the Maxwell equations and the Lorentz force for arbitrary values of $r$, $n$, and $k$ are postulated in terms of interior and exterior derivatives, in a form that closely resembles their vector-calculus analogues. These formulas lead to solutions in terms of potentials of grade $r-1$, and to conservation laws in terms of a stress-energy-momentum tensor of rank 2 for any values of $r$, $n$, and $k$, for which a simple explicit formula is given. As an application, an expression for the flux of the stress-energy-momentum tensor across an $(n+k-1)$-dimensional slice of space-time is given in terms of the Fourier transform of the potentials. The abstraction of Maxwell equations with exterior calculus combines the simplicity and intuitiveness of vector calculus, as the formulas admit explicit expressions, with the power of tensors and differential forms, as the formulas can be given for any values of $r$, $n$, and $k$. Comment: 26 pages, 2 figures. In this paper, with respect to the published version, Eq. (35) has been corrected with a different sign of a term. The procedure followed in Appendix 1.2 is not fully correct, despite the result is. The correct procedure is presented in Sect. 3.6 of Eur. Phys. J. Plus 136, 212 (2021), (arXiv:2104.07013) |
| Databáze: | OpenAIRE |
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