This 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, ...
This 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.
+