More on the Subtraction Algorithm

Abstract

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $\delta \lambda$ of the parameters $\lambda$ of the classical Lagrangian and canonical transformations, by generalizing a well- known conjecture on the form of the divergent terms. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space ${\mathcal{M}}_{gf}$ of the gauge-fixing parameters. A principal fiber bundle $\mathcal{E}\to {\mathcal{M}}_{gf}$ with a connection ${\omega }_1$ is defined, such that the canonical transformations are gauge transformations for ${\omega }_1$. This provides an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on ${\mathcal{M}}_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space ${\mathcal{M}}_{ph}$ of the physical parameters $\lambda$ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on ${\mathcal{M}}_{ph}$, orthogonal to ${\mathcal{M}}_{gf}$ (under which the action transforms as a scalar), and gauge transformations on $\mathcal{E}$. 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.

LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/EP

References in corpus (1)

• Predictivity and Nonrenormalizability

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