Perturbative Quantum Gravity Coupled to Particles in (1+1)-Dimensions

TL;DR

This paper develops a quantum gravity model in (1+1) dimensions coupled with particles, deriving energy corrections and wavefunctions, revealing weaker binding than in classical Newtonian gravity.

Contribution

It provides the first explicit post-Newtonian quantum corrections for a (1+1)-dimensional gravity-particle system, including wavefunction perturbations.

Findings

Particles are less tightly bound than in classical Newtonian gravity.

Explicit second-order energy corrections are computed.

Perturbed wavefunctions are explicitly derived.

Abstract

We consider the problem of (1+1)-dimensional quantum gravity coupled to particles. Working with the canonically reduced Hamiltonian, we obtain its post-Newtonian expansion for two identical particles. We quantize the (1+1)-dimensional Newtonian system first, after which explicit energy corrections to second order in 1/c are obtained. We compute the perturbed wavefunctions and show that the particles are bound less tightly together than in the Newtonian case.