Abstract :
[en] The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold S of a Poisson manifold (M, \Pi).
However the assignment (coisotropic submanifold) -> (differential graded Poisson algebra) is not canonical, since in the construction several choices have to be made. One has to fix: 1. an embedding of the normal bundle NS of S into M as a tubular neighbourhood, 2. a connection on NS and 3. a special element Omega.
We show that different choices of a connection and an element Omega -- but
with the tubular neighbourhood fixed -- lead to isomorphic differential graded Poisson algebras. If the tubular neighbourhood is changed too, invariance can be restored at the level of germs.
Funders :
University of Zurich (Zurich, Switzerland)
Swiss National Science Foundation (SNF-grant 200020-121640/1)
European Union through the FP6 Marie Curie RTN ENIGMA (contract number MRTN-CT-2004-5652)
European Science Foundation through the MISGAM program
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