Symmetries of scalar fields. II

Local symmetries and conserved densities are calculated for a system of classical scalar fields in $(n+1)$-dimensional ($n>1$) space-time with Lagrangian of the form
$$ L=\frac12h_{ab}(\varphi){\varphi_\nu}^a\varphi^{b\nu}-V(\varphi). $$
It is shown that, in contrast to two-dimensional theories, the existence of higher symmetries or conservation laws is possible only if in the field equations one can separate a linear subsystem by means of a point transformation $\varphi^a=f^a(\bar\varphi)$. In the case of an irreducible metric $h_{ab}$, all symmetries and conserved densities are found explicitly. An equation is obtained for the local conserved densities of an arbitrary generalized-evolution system.