Problems of functional determinant and fictitious lagrangian in gauge theories

Abstract

Using the method of Lagrange multiplier fields the fictitious Lagrangian of gauge-fixed gauge theories can be constructed. We obtain different but equivalent forms depending on the extent to which constraint equations are used. These constructions yield fictitious Lagrangians which restore unitarity and gauge invariance. The usual method of constructing fictitious Lagrangians using the change of gauge conditions under gauge transformations does not always lead to the same fictitious Lagrangian constructed by the above method. They are, however, related by an interchange of fictitious fields and lead to the same amplitudes. We also discuss a scale transformation of the fictitious fields, which changes the explicit form of the fictitious Lagrangian but not its amplitudes. In the course of this study we display certain technical problems in the definition of the functional determinants related to a fictitious Lagrangian.