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.
MORE ON THE SUBTRACTION ALGORITHM
ANSELMI, DAMIANO
1995-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.