ar X iv : h ep - t h / 99 01 12 5 v 2 2 6 Ja n 19 99 BRX TH – 449 CTP # 2818 Higher Derivative Chern – Simons Extensions

We study the higher-derivative extensions of the D=3 Abelian Chern–Simons topological invariant that would appear in a perturbative effective action's momentum expansion. The leading, third-derivative, extension I ECS turns out to be unique. It remains parity-odd but depends only on the field strength, hence no longer carries large gauge information, nor is it topological because metric dependence accompanies the additional covariant derivatives, whose positions are seen to be fixed by gauge invariance. Viewed as an independent action, I ECS requires the field strength to obey the wave equation. The more interesting model, adjoining I ECS to the Maxwell action, describes a pair of excitations. One is massless, the other a massive ghost, as we exhibit both via the propagator and by performing the Hamiltonian decomposition. We also present this model's total stress tensor and energy. Other actions involving I ECS are also noted.