Dynamical Ambiguities in Singular Gravitational Field

TL;DR

This paper investigates the effects of singularities on particle dynamics in gravitational fields, showing how including singularities can resolve quantization ambiguities and lead to a unique quantum description.

Contribution

It demonstrates that incorporating singularities in 2D gravitational systems restores global symmetry and removes quantization ambiguities.

Findings

Including singularities yields a global SO(2.1) symmetry.

Quantization with singularities produces a unique quantum theory.

Without singularities, the system's symmetry is only local, causing ambiguities.

Abstract

We consider particle dynamics in singular gravitational field. In 2d spacetime the system splits into two independent gravitational systems without singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but the corresponding symmetry transformations are not defined globally. Quantization leads to ambiguity. By including singularity one can get the global $SO(2.1)$ symmetry. Quantization in this case leads to unique quantum theory.