String-Inspired Gravity with Interacting Point Particles

Abstract

We reformulate two dimensional string-inspired gravity with point particles as a gauge theory of the extended Poincar\'e group. A non-minimal gauge coupling is necessary for the equivalence of the two descriptions. The classical one-particle problem is analyzed completely. In addition, we obtain the many-particle effective action after eliminating the gravity degrees of freedom. We investigate properties of this effective action, and show how to recover the geometrical description. Quantization of the gauge-theoretic model is carried out and the explicit one-particle solution is found. However, we show that the formulation leads to a quantum mechanical inconsistency in the two-particle case. Possible cures are discussed.