A Comparison of the Proper Time Equation and the Renormalization Group $β$-Function in String Theory

Details A Comparison of the Proper Time Equation and the Renormalization Group $β$-Function in String Theory A Comparison of the Proper Time Equation and the Renormalization Group $β$-Function in String Theory

1995-05-22

arxiv.org/abs/hep-th/9505134v2

Mod. Phys. Lett. A10 (1995) 1565

Physics

High Energy Physics

High Energy Physics - Theory

Latex File, 15 pages. Revised version, to appear in Mod. Phys. Lett. A. Some minor misprints corrected and a reference added

Scientific paper

10.1142/S021773239500168X

It is known that there is a proportionality factor relating the $\beta$-function and the equations of motion viz. the Zamolodchikov metric. Usually this factor has to be obtained by other methods. The proper time equation, on the other hand, is the full equation of motion. We explain the reasons for this and illustrate it by calculating corrections to Maxwell's equation. The corrections are calculated to cubic order in the field strength, but are exact to all orders in derivatives. We also test the gauge covariance of the proper time method by calculating higher (covariant) derivative corrections to the Yang-Mills equation.

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