Special properties of
The string form defined by Eq. (3) is very special.
Besides it satisfies, for any ,
the following special properties:
where corresponds to the BV Laplacian w.r.to the halfdensity .
Eqs (4) and (5) are very special. They imply:
Therefore, the equivariant analogue of in the Cartan model can be constructed
as follows:

The construction of the Cartan equivariant form is recast as a
construction of a representation of in functions on BV phase space.
In other words, we need a morphism
(where is the Lie superalgebra of infinitesimal BVcanonical transformations)
such that agrees with
(remember is the same as ).
We denote it like this: