On the angular momentum and spin of generalized electromagnetic field for r-vectors in (k, n) space-time dimensions

Abstract This paper studies the relativistic angular momentum for generalized electromagnetic field, described by r -vectors in ( k , n ) space-time dimensions, with exterior-algebraic methods. First, angular-momentum tensor is derived from invariance of Lagrangian to rotations (Lorentz transformations), avoiding explicit need canonical Noether’s theorem. The derivation proves conservation law generic values and . Second, an integral expression flux across a $$(k+n-1)$$ (k+n-1) -dimensional surface constant $$\ell $$ xmlns:mml="http://www.w3.org/1998/Math/MathML">ℓ -th coordinate provided terms normal modes field; this analysis natural generalization standard electromagnetism, i. e. three-dimensional space at time. Third, brief discussion on orbital spin including their complex-valued circular polarizations,