On vector-tensor minimally coupled field theories (Q1073369)

The paper is concerned with the theory of classical source-free electromagnetic fields on Riemannian manifolds. It is assumed that the Lagrangian consists of the sum of two terms, one of which is the scalar curvature density, while the second depends on the metric tensor, a covector field \(\psi\), and the first derivatives of the components of the latter (minimal coupling). The authors investigate the conditions under which the invariance of various Euler-Lagrange tensor densities under gauge transformations \(\psi_ j\to \psi_ j+\phi_ j\) implies the invariance of the Lagrangians. Moreover, characterizations are given of Lagrangians whose Euler-Lagrange densities vanish identically.