Quantization of Even-Dimensional Actions of Chern-Simons Form with Infinite Reducibility

Abstract

We investigate the quantization of even-dimensional topological actions of Chern-Simons form which were proposed previously. 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 infinite number of ghosts and antighosts. The minimal actions of 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 shown that the gauge-fixed actions of both formulations coincide even though the classical action breaks Dirac's regularity condition. We find an interesting relation that the BRST charge of Hamiltonian formulation is the odd-dimensional fermionic counterpart of the topological action of Chern-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.