One of the key differences between the (anti-)BRST and (anti-)co-BRST symmetries is that the former symmetries leave the kinetic term invariant whereas under the latter symmetries the gauge-fixing term remains invariant.
The (anti-)BRST invariant Lagrangian for the Christ-Lee model that incorporates the gauge-fixing term and Faddeev-Popov (anti-)ghost variables can be written as [19, 24]
The gauge-fixing term ([??] + 0), which remains invariant under (anti-)co-BRST symmetries, can be written in the following fashion:
The invariance of gauge-fixing term under the (anti-)co-BRST transformations can be captured in the following (anti)co-BRST invariant restriction [17, 28]
Before we wrap this section, we point out that the total gauge-fixing term (1/2)[b.sup.2] + b([??] - [theta]) remains invariant under (anti-)co-BRST transformations.
As we already know that the total gauge-fixing term [b.sup.2]/2+ b([??] + [theta]) is (anti-)co-BRST invariant [cf.