Stable interactions in higher derivative field theories of derived type

Abstract: We consider the general higher derivative field theories of derived type. At free level, the wave operator of derived-type theory is a polynomial of the order $n\geq 2$ of another operator $W$ which is of the lower order. Every symmetry of $W$ gives rise to the series of independent higher order symmetries of the field equations of derived system. In its turn, these symmetries give rise to the series of independent conserved quantities. In particular, the translation invariance of operator $W$ results in the series of conserved tensors of the derived theory. The series involves $n$ independent conserved tensors including canonical energy-momentum. Even if the canonical energy is unbounded, the other conserved tensors in the series can be bounded, that will make the dynamics stable. The general procedure is worked out to switch on the interactions such that the stability persists beyond the free level. The stable interaction vertices are inevitably non-Lagrangian. The stable theory, however, can admit consistent quantization. The general construction is exemplified by the order $N$ extension of Chern-Simons coupled to the Pais-Uhlenbeck-type higher derivative complex scalar field.