In BV formalism we can consider a Lagrangian submanifold as a gauge
condition. Starting with the BV action functional we construct a closed form on
the space of Lagrangian submanifolds...If the action functional is invariant
with respect to some group $H$ and $\Lambda$ is an $H$-invariant family of
Lagrangian submanifold then under certain conditions we construct a form on
$\Lambda$ that descends to a closed form on $\Lambda/H.$ Integrating the latter
form over a cycle in $\Lambda/H$ we obtain numbers that can have interesting
physical meaning. We show that one can get string amplitudes this way. Applying
this construction to topological quantum field theories one obtains topological
invariants.(read more)