Quantization of even-dimensional actions of Chern-Simons form with infinite reducibility Original Research Article

We investigate the quantization of even-dimensional topological actions of Chern-Simons from which have been proposed earlier. We quantize the actions by Lagrangian and Hamiltonian formulations à la Batalin, Fradkin and Vilkovisky. The models turn out to be infinitely reducible and thus we need an infinite number of ghosts and antighosts. The minimal actions of the Lagrangian formulation which satisfy the master equation of Batalin and Vilkovisky have the same Chern-Simons form as the starting classical actions. In the Hamiltonian formulation we have used the formulation of cohomological perturbation and explicitly show that the gauge-fixed actions of both formulations coincide even though the classical action breaks Diracʹs regularity condition. We find the interesting relation that the BRST charge of the Hamiltonian formulation is the odd-dimensional fermionic counterpart of the topological action of Chem-Simons form. Although the quantization of two-dimensional models which include both bosonic and fermionic gauge fields are investigated in detail, it is straightforward to extend the quantization into arbitrary even dimensions. This completes the quantization of previously proposed topological gravities in two and four dimensions.