Form 
Let us study the whole equivalence class of theories. It is infinite-dimensional,
because there Let us choose a basis
; the space of BRST trivial deformations is parametrized by the coordinates
:
Let us call this equivalence class
. It turns out that the following differential form on
is closed:
|
|
We want to obtain BRST invariants by integrating
Problems:
Usually the operator
is only nilpotent on-shell; this requires more careful (than Eq. (1)) definition of a deformation
It appears that
is not well-defined, because if
is BRST-closed, it does not deform the action, and yet the form is nonzero
Solution: We should use the BV formalism.
We will now switch to BV language