Let us study the whole equivalence class
of theories. It is infinite-dimensional,
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
Let us call this equivalence class
. It turns out that the following differential form on
a pseudo-differential form on
We want to obtain BRST invariants by integrating
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
We should use the BV formalism.
We will now switch to BV language