Extension of the Chern–Simons Theory: Conservation Laws, Lagrange Structures, and Stability

We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern–Simons operator. For the nth order theory of this type, we provide a covariant procedure for constructing n-parameter family of conservation laws associated with spatiotemporal symmetries. This family includes the canonical energy that is unbounded from below, whereas others conservation laws from the family can be bounded from below for certain combinations of the Lagrangian parameters, even though higher derivatives are present in the Lagrangian. We prove that any conserved quantity bounded from below is related with invariance of the theory with respect to the time translations and ensures the stability of the model.