We present an exact derivation of conserved tensors associated to the higher-order symmetries in the higher derivative Abelian gauge field theories. In our model, the wave operator of the derived theory is a n-th order polynomial expressed in terms of the usual Maxwell operator. Relying on this formalism and utilizing the extension of Noether's theorem, we acquire a series of conserved second-rank tensors which includes the standard canonical energy-momentum tensors. Moreover, with the aid of auxiliary fields, we succeed in obtaining the relations between the root decomposition of characteristic polynomial of the wave operator and the conserved energy-momentum tensors in the context of another equivalent lower-order representation. Under the certain conditions, although the canonical energy of the higher derivative dynamics is unbounded from below, the 00-component of the linear combination of these conserved quantities is bounded. By this reason, the original derived theory is considered stable. Finally, as an instructive example, we elaborate the third-order derived system and analyze the stabilities in different cases of root decomposition of the characteristic polynomial extensively.

我们提出了与高导阿贝尔规范场理论中的高阶对称性相关的守恒张量的精确推导。在我们的模型中，推导理论的波算子是n用通常的麦克斯韦算子表示的二阶多项式。依靠这种形式主义并利用Noether定理的扩展，我们获得了一系列守恒的二阶张量，其中包括标准的规范能量动量张量。此外，借助辅助场，我们成功地获得了在另一种等效的低阶表示形式下，波动算子的特征多项式的根分解与守恒的能量动量张量之间的关系。在某些条件下，尽管较高的导数动力学的规范能量从下方不受限制，但这些守恒量的线性组合的00分量是有界的。因此，原始派生理论被认为是稳定的。最后，作为一个指导性的例子，