  The quantum master equation is usually formulated in terms of functionals of
the components of mappings from a space-time manifold M into a
finite-dimensional vector space. The master equation is the sum of two terms
one of which is the anti-bracket (odd Poisson bracket) of functionals and the
other is the Laplacian of a functional. Both of these terms seem to depend on
the fact that the mappings on which the functionals act are vector-valued. It
turns out that neither this Laplacian nor the anti-bracket is well-defined for
sections of an arbitrary vector bundle. We show that if the functionals are
permitted to have their values in an appropriate graded tensor algebra whose
factors are the dual of the space of smooth functions on M, then both the
anti-bracket and the Laplace operator can be invariantly defined. Additionally,
one obtains a new anti-bracket for ordinary functionals.
