MORE ON THE SUBTRACTION ALGORITHM

We continue the programme of investigating the removal of divergences of a generic quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebras a recently formulated algorithm, based on redefinitions delta lambda of the parameters lambda of the classical Lagrangian and canonical transformations. The key point is to generalize a well known conjecture on the form of the divergent terms to the case of open gauge-algebras. We, also show that it is possible to obtain complete control over the effects of the subtraction algorithm on the space M(gf) Of the gauge-fixing parameters. We develop a differential calculus on M(gf) providing an intuitive geometrical description of the fact that the on-shell physical amplitudes cannot depend on M(gf). A principal fibre bundle epsilon --> M(gf) With a connection or is defined such that the canonical transformations are gauge transformations for omega(1). A geometrical description of the effect of the subtraction algorithm on the space M(ph) Of the physical parameters lambda is also proposed. Finally, the full subtraction algorithm is described as a series of diffeomorphisms on M(ph), orthogonal to M(gf) (under which the action transforms as a scalar), and gauge transformations on epsilon. In this geometrical context, a suitable concept of predictivity is formulated. We give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.