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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 of the parameters 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 of the gauge-fixing parameters. We develop a differential calculus on providing an intuitive geometrical description of the fact that the on-shell physical amplitudes cannot depend on . A principal fibre bundle with a connection is defined such that the canonical transformations are gauge transformations for . A geometrical description of the effect of the subtraction algorithm on the space of the physical parameters is also proposed. Finally, the full subtraction algorithm is described as a series of diffeomorphisms on , orthogonal to (under which the action transforms as a scalar), and gauge transformations on . 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.