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

TL;DR

This paper explores the quantization of two-dimensional generalized Chern-Simons actions, revealing their infinite reducibility and demonstrating a unified quaternion-based approach to manage the infinite fields, with implications for higher dimensions.

Contribution

It introduces a method to quantize infinitely reducible generalized Chern-Simons models using quaternion algebra, extending the approach to arbitrary even dimensions.

Findings

Successfully quantized 2D generalized Chern-Simons models

Controlled infinite fields with quaternion algebra

Extended quantization framework to higher even dimensions

Abstract

We investigate the quantization of 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 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.