Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-07-05
Class.Quant.Grav.12:319-350,1995
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/EP
Scientific paper
10.1088/0264-9381/12/2/005
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 ${\cal M}_{gf}$ of the gauge-fixing parameters. A principal fiber bundle ${\cal E}\rightarrow {\cal M}_{gf}$ 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 ${\cal M}_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space ${\cal M}_{ph}$ of the physical parameters $\lambda$ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on ${\cal M}_{ph}$, orthogonal to ${\cal M}_{gf}$ (under which the action transforms as a scalar), and gauge transformations on ${\cal E}$. 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.
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