Our stratedy

  • Interpret the standard BRST complex as a Lie algebra cohomology complex for some infinite-dimensional Lie algebra; actually we will need the so-called relative Lie algebra cohomology

  • This relative cohomology can be interpreted as the cohomology (usual, not relative; and with trivial coefficients) of some ideal, which is defined similarly to the ideal of the Maxwell theory

We can do this for both and flat space.