On electromagnetism and generalized energy-momentum tensor of the electromagnetic field in spaces with Finsler geometry

Abstract

By using variational calculus and exterior derivative formalism, we proposed in two previous joint papers with S. Siparov a new geometric approach for electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge invariance. Also, for flat pseudo-Finsler spaces, we define a generalized energy-momentum tensor (consisting of two blocks), as the symmetrized Noether current corresponding to the invariance of the field Lagrangian with respect to spacetime translations. In curved spaces, one of the blocks of the generalized energy-momentum tensor is obtained by varying the field Lagrangian with respect to the metric tensor and the other one, by varying the same Lagrangian with respect to the nonlinear connection.