String-Inspired Gravity with Interacting Point Particles

TL;DR

This paper reformulates 2D string-inspired gravity with point particles as a gauge theory, analyzes classical and quantum solutions, and discusses inconsistencies in multi-particle quantum cases.

Contribution

It introduces a gauge-theoretic formulation of string-inspired gravity with point particles, including classical solutions and quantum analysis, highlighting quantum inconsistencies in multi-particle scenarios.

Findings

Classical one-particle solutions are fully analyzed.

Effective multi-particle action is derived and related to geometrical descriptions.

Quantum inconsistency arises in the two-particle case, with potential remedies discussed.

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.