The Proper Time Equation and the Zamolodchikov Metric
Abstract
The connection between the proper time equation and the Zamolodchikov metric is discussed. The connection is two-fold: First, as already known, the proper time equation is the product of the Zamolodchikov metric and the renormalization group beta function. Second, the condition that the two-point function is the Zamolodchikov metric, implies the proper time equation. We study the massless vector of the open string in detail. In the exactly calculable case of a uniform electromgnetic field strength we recover the Born-Infeld equation. We describe the systematics of the perturbative evaluation of the gauge invariant proper time equation for the massless vector field. The method is valid for non-uniform fields and gives results that are exact to all orders in derivatives. As a non trivial check, we show that in the limit of uniform fields it reproduces the lowest order Born-Infeld equation.
Keywords
Cite
@article{arxiv.hep-th/9509097,
title = {The Proper Time Equation and the Zamolodchikov Metric},
author = {B. Sathiapalan},
journal= {arXiv preprint arXiv:hep-th/9509097},
year = {2009}
}
Comments
Latex file, 29 pages, A couple of minor typos corrected. Final version, to appear in Int. Journal of Mod. Phys.A