Solutions to a Quantal Gravity-Matter Field Theory on a Line

TL;DR

This paper explores solutions to a quantum gravity-matter field theory involving a scalar-tensor model, addressing anomalies in the quantization process by modifying the Wheeler--DeWitt equation, leading to multiple physical spectra.

Contribution

It introduces modifications to the Wheeler--DeWitt equation to resolve quantal anomalies in scalar-tensor quantum gravity interacting with matter.

Findings

Anomalies prevent straightforward Dirac quantization.

Modified Wheeler--DeWitt equations eliminate anomalies.

Multiple physical spectra arise from different modifications.

Abstract

Solutions to a scalar-tensor (dilaton) quantum gravity theory, interacting with quantized matter, are described. Dirac quantization is frustrated by quantal anomalies in the constraint algebra. Progress is made only after the Wheeler--DeWitt equation is modified by quantal terms, which eliminate the anomaly. More than one modification is possible, resulting in more than one `physical' spectrum in the quantum theory, corresponding to the given classical model.