Star Product Reduction for Coisotropic Submanifolds of Codimension 1

We propose a reduction procedure that leads to a reduced star product on the reduced phase space of a `First Class'-constrained system, where no symmetries, group actions or the like are present. For the case that the coisotropic submanifold has codimension 1, we establish a constructive method to compute the reduced star product explicitly. Concluding examples show that this method depends crucially on the constraint function singled out to describe the constrained submanifold and not only on this submanifold itself, and that two different constraint functions for the same constraint submanifold will generally result in not only different but inequivalent reduced star products.