Ordinary 
1 Definition of
Remember that the set of fields 
consists of the “classical” fields 
,
plus ghosts 
, plus BRST quartets.
consists of the “classical” fields ,
plus ghosts , plus BRST quartets.
2 Symmetries
Symmetries correspond to those 
which are BRST exact plus equations of motion.
In other words, for any vector field 
on the field space and any functional
the following 
should correspond to a symmetry:
which are BRST exact plus equations of motion.
In other words, for any vector field on the field space and any functional
the following should correspond to a symmetry:
The second term on the RHS,
, can be interpreted as the term
which vanish on-shell, plus
which combines with the first term
.
3 No horizontality
The form given by Eq. (1) is not horizontal, but the contraction is an exact form:
given by Eq. (1) is not horizontal, but the contraction is an exact form:
On the next page we will discuss the equivariant form.