Equivalence classes of theories
Many physical theories have BRST-like structure. This means that there is a nilpotent fermionic
symmetry 
, and the space of physical states is the cohomology of .Such theories come with an equivalence relation. Physically, the theory with the action 
is equivalent to the theory with the action 
for any operator 
. Physically
meaningful quantities should be invariant, i.e. should not change under this
equivalence transformation. Important question is:
is equivalent to the theory with the action for any operator . Physically
meaningful quantities should be invariant, i.e. should not change under this
equivalence transformation. Important question is:
how can we obtain such invariants?
Naively it would seem that the only way to obtain an invariant is to take the path integral:
|
where 
are some BRST-closed operators.
are some BRST-closed operators.But actually there are other possibilities, which we will now describe.