Stability in the higher derivative Abelian gauge field theories

Abstract

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.