Generalized Killing Tensors and Symmetry of Klein-Gordon-Fock Equations

Abstract

The paper studies non-Lie symmetry of the Klein-Gordon-Fock equation (KGF) in $(p+q)$-dimensional Minkowsky space. Full set of symmetry operators for the $n$-order KGF equation was explicitly calculated for arbitrary $n<\infty$ and $p+q \leq 4$. Definition was given for generalized Killing tensors of rank $j$ and order $s$, and for generalized conformal Killing tensors of rank $j$ and order $s$ as a complete set of linearly independent solutions of some overdetermined systems of PDE. These tensors were found in explicit form for arbitrary fixed $j$ and $s$ in Minkowsky space of dimension $p+q \leq 4$. The received results can be used in investigation of higher symmetries of a wide class of systems of partial differential equations.