Canonical choice of 
in standard BRST formalism
A special case of the BV formalism is the “standard” BRST formalism. It works for such theories as
Yang-Mills/QCD, and also for the bosonic string worldsheet theory
and the RNS superstring.
The most important property of such theories is the existence of a fermionic “BRST symmetry”
which is nilpotent off-shell (i.e. nilpotent without using the equations of motion).
Here we will briefly review these standard BRST theories, and show that in this case exists a natural
choice for 
.
1 Brief review of the “standard” BRST formalism
where
are collective notation for the “classical fields” (in the case
of Yang-Mills theory they would be the gauge fields
).
2 Standard choice of
In this case we can choose
to be the space of expressions:
where
is the parameter of the gauge symmetry.
The resulting algebra
is the algebra of gauge symmetries of the original
which we started with. Indeed,
is just the odd Hamiltonian of
the gauge symmetries:
3 Equivariant 
in BRST case
3.1 General formula
3.2 Special case of bosonic string
| | | | |
| where  |
| |  where  ’s parametrize the family  of LAGs
|
|
| | |
Usually
.
