Batalin–Fradkin Approach to (1 + 1)-Dimensional Massive Vector Fields and the Gluonic Effective Action for Hard Thermal Loops

Abstract

The Lagrangian of (1 + 1)-dimensional massive vector fields is studied. Since this system has second class constraints, the method of Batalin–Fradkin, which introduces new fields to convert second class constraints into first class ones, is applied in an extended manner. Instead of the usual treatment, which uses the Stueckelberg field as a new field, we can use a pseudoscalar field. We will show there are at least two ways to introduce a pseudoscalar. At the quantum level, one way leads to the system that is equivalent to the original system, and the other way gives an inequivalent system. The relation of these two ways is clarified. As an application of the latter way, we consider QCD at finite temperature and the gluonic effective action for hard thermal loops is constructed.