On this page:
1 Brief review of the “standard” BRST formalism
2 Standard choice of
3 Equivariant in BRST case
3.1 General formula
3.2 Special case of bosonic string

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

    2 Standard choice of

    3 Equivariant in BRST case

      3.1 General formula

      3.2 Special case of bosonic string

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:

(40)

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 .