Extended Lagrangian theory of electromagnetism (Q921606)

A Lagrange space is a differentiable manifold M endowed with a regular Lagrangian L: TM\(\to R\) [see \textit{J. Kern}, Arch Math. 25, 438-443 (1974; Zbl 0297.53035)]. In the present paper, the well-known Lagrangian of relativistic electrodynamics \[ L_ 0(x,y)=\sqrt{a_{ij}(x)y^ iy^ j}+\frac{e}{mc^ 2}A_ i(x)y^ i, \] is replaced in turn by \[ L_ 1(x,y)=a_{ij}(x)y^ iy^ j+\frac{2e}{mc^ 2}A_ i(x)y^ i,\text{ and } L_ 2(x,y)=g_{ij}(x,y)y^ iy^ j+A_ i(x)y^ i+U(x), \] where \(g_{ij}\) is a (0)-homogeneous fundamental metric tensor on M and U is a scalar field on M. The authors define an extended electromagnetic tensor field and obtain some generalized Maxwell equations. The study is based on Finsler geometry and its generalization to Lagrange spaces.