The Batalin–Vilkovisky–Fradkin
(BFV) formalism, introduced to handle classical systems equipped with symmetries,
associates a differential graded Poisson algebra to any coisotropic submanifold S of a
Poisson manifold (M,Π). However, the assignment given by mapping a coisotropic
submanifold to a differential graded Poisson algebra is not canonical since in the
construction several choices have to be made. One has to fix an embedding of the
normal bundle NS of S into M as a tubular neighborhood, a connection ∇ on NS,
and a special element Ω.
We show that different choices of a connection and an element Ω—but with the
tubular neighborhood fixed—lead to isomorphic differential graded Poisson algebras.
If the tubular neighborhood is changed as well, invariance can still be restored at the
level of germs.
