Martínez, Alfonso, 1973-Colombaro, IvanoFont Segura, Josep2022-05-182022-05-182021Martinez A, Colombaro I, Font-Segura J. On the angular momentum and spin of generalized electromagnetic field for r-vectors in (k, n) space-time dimensions. Eur Phys J Plus. 2021;136:1047. DOI: 10.1140/epjp/s13360-021-02023-52190-5444http://hdl.handle.net/10230/53128This paper studies the relativistic angular momentum for the generalized electromagnetic field, described by r-vectors in (k, n) space-time dimensions, with exterioralgebraic methods. First, the angular-momentum tensor is derived from the invariance of the Lagrangian to space-time rotations (Lorentz transformations), avoiding the explicit need of the canonical tensor in Noether’s theorem. The derivation proves the conservation law of angular momentum for generic values of r, k, and n. Second, an integral expression for the flux of the tensor across a (k + n − 1)-dimensional surface of constant -th space-time coordinate is provided in terms of the normal modes of the field; this analysis is a natural generalization of the standard analysis of electromagnetism, i. e. a three-dimensional space integral at constant time. Third, a brief discussion on the orbital angular momentum and the spin of the generalized electromagnetic field, including their expression in complex-valued circular polarizations, is provided for generic values of r, k, and n.application/pdfeng© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Àlgebrainfo:eu-repo/semantics/articlehttp://doi.org/10.1140/epjp/s13360-021-02023-5info:eu-repo/semantics/openAccess