Predictivity and Nonrenormalizability

Abstract

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.

31 pages, LaTeX, SISSA/ISAS 147/93/EP (An alternative proof of a lemma in sect. V has been added. Minor changes in some comments in Introduction and sections IV and V. References added.)

References in corpus (7)

• Geometry of Batalin-Vilkovisky quantization
• Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
• Topological Sigma-Models in Four Dimensions and Triholomorphic Maps
• Origin of Antifields in the Batalin-Vilkovisky Lagrangian Formalism
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• More on the Subtraction Algorithm
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• Classical and quantum aspects of the extended antifield formalism
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