Quantum States of String-Inspired Lineal Gravity

TL;DR

This paper constructs quantum states for a (1+1)-dimensional gravity-matter gauge theory based on the extended Poincaré group, revealing gauge-invariant wave functionals with a phase factor but no evidence of gravity-matter forces.

Contribution

It provides explicit formulas for quantum states in a (1+1)D gravity-matter model with a gauge theory structure based on the extended Poincaré group.

Findings

Wave functionals are gauge invariant up to a phase factor.

No evidence of gravity-matter forces was observed.

Explicit formulas for quantum states were derived.

Abstract

We construct quantum states for a (1+1) dimensional gravity-matter model that is also a gauge theory based on the centrally extended Poincar\'e group. Explicit formulas are found, which exhibit interesting structures. For example wave functionals are gauge invariant except for a gauge non-invariant phase factor that is the Kirillov-Kostant 1-form on the (co-) adjoint orbit of the group. However no evidence for gravity-matter forces is found.