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arXiv math-ph/0506002math-phmath.MP
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Klein-Gordon-Fock方程的广义Killing张量和对称性

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

Anatoly G. Nikitin, Oleksander I. Prylypko

备注：
The first version of the paper was published as a preprint in Russian: Preprint N 90.23, Kyiv, Institute of Mathematics, 1990, 59 p
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摘要：

研究了$(p+q)$维Minkowsky空间中Klein-Gordon-Fock方程（KGF）的非Lie对称性.对于任意的$n<\infty$和$p+q \leq 4$，计算了$n$阶KGF方程的对称算符.定义了秩为$j$、阶为$s$的广义Killing张量和秩为$j$、阶为$s$的广义共形Killing张量为一类超定偏微分方程组的线性无关解的完备集.对于任意固定的$j$和$s$，在$p+q \leq 4$维的Minkowsky空间中，这些张量以显式形式存在.所得结果可用于研究一类广泛的偏微分方程系统的高阶对称性。

英文摘要：

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.

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