Form 
Let us study the whole equivalence class of theories. It is infinite-dimensional,
because there 
where 
could be more or less arbitrary functional.
There are infinitely many possible .Let us choose a basis 
; the space of BRST trivial deformations is parametrized by the coordinates 
:
; 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:
. It turns out that the following differential form on is closed:
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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 deformationIt 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