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 YangMills/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 offshell (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
The usual translation of the BRST formalism into the BV language leads to the following Master Action:
where are collective notation for the “classical fields” (in the case
of YangMills 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


Usually .