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 stre ngth, hence no longer carries large gauge information, nor is it topologica l because metric dependence accompanies the additional covariant derivative s, whose positions are seen to be fixed by gauge invariance. Viewed as an i ndependent action, I-ECS requires the field strength to obey the wave equat ion. The more interesting model. adjoining I-ECS to the Maxwell action, des cribes a pair of excitations. One is massless, the other a massive ghost, a s we exhibit both via the propagator and by performing the Hamiltonian deco mposition. We also present this model's total stress tensor and energy. Oth er actions involving I-ECS are noted, as is the corresponding extension of the D = 4 theta- term. (C) 1999 Elsevier Science B.V. All rights reserved.