The Proper Time Equation and the Zamolodchikov Metric

Details The Proper Time Equation and the Zamolodchikov Metric The Proper Time Equation and the Zamolodchikov Metric

1995-09-16

arxiv.org/abs/hep-th/9509097v2

Int.J.Mod.Phys. A11 (1996) 2887-2906

Physics

High Energy Physics

High Energy Physics - Theory

Latex file, 29 pages, A couple of minor typos corrected. Final version, to appear in Int. Journal of Mod. Phys.A

Scientific paper

10.1142/S0217751X96001401

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.

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