Form
Let us study the whole equivalence class of theories. It is infinitedimensional,
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 :
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 onshell; this requires more careful (than Eq. (1)) definition of a deformation
It appears that is not welldefined, because if is BRSTclosed, 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