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arXiv · hep-th/9509097

The Proper Time Equation and the Zamolodchikov Metric

B. Sathiapalan
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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.

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B. Sathiapalan. 1995-11-30. The Proper Time Equation and the Zamolodchikov Metric. https://doi.org/10.1142/s0217751x96001401

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