Predictivity and Nonrenormalizability

Details Predictivity and Nonrenormalizability Predictivity and Nonrenormalizability

1993-09-15

arxiv.org/abs/hep-th/9309085v3

Class.Quant.Grav. 11 (1994) 2181-2204

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, LaTeX, SISSA/ISAS 147/93/EP (An alternative proof of a lemma in sect. V has been added. Minor changes in some commen

Scientific paper

10.1088/0264-9381/11/9/005

We consider the problem of removing the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable). We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of some parameters (possibly infinitely many) and a canonical transformation (in the sense of Batalin and Vilkovisky) of fields and BRS sources. Gauge-invariance is turned into a suitable quantum generalization of BRS-invariance. We define quantum observables and study their properties. We apply the result to renormalizable gauge-field theories that are gauge-fixed with a nonrenormalizable gauge-fixing and prove that their predictivity is retained. A corollary is that topological field theories are predictive. Analogies and differences with the formalisms of classical and quantum mechanics are pointed out.

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