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.
Cite
@article{arxiv.hep-th/9309085,
title = {Predictivity and Nonrenormalizability},
author = {Damiano Anselmi},
journal= {arXiv preprint arXiv:hep-th/9309085},
year = {2009}
}
Comments
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.)