Quantization of Infinitely Reducible Generalized Chern–Simons Actions in Two Dimensions

Abstract:

We investigate the quantization of the two-dimensional version of the generalized Chern–Simons actions which were proposed previously. The models turn out to be infinitely reducible and thus we need an infinite number of ghosts, antighosts and the corresponding antifields. The quantized minimal actions which satisfy the master equation of Batalin and Vilkovisky have the same Chern–Simons form. The infinite fields and antifields are successfully controlled by the unified treatment of generalized fields with quaternion algebra. This is a universal feature of generalized Chern–Simons theory and thus the quantization procedure can be naturally extended to arbitrary even dimensions.