Area-preserving Structure and Anomalies in 1+1-dimensional Quantum Gravity

TL;DR

This paper compares two formulations of 1+1-dimensional quantum gravity, showing they are essentially equivalent despite technical differences, and explores their gauge independence and anomalies.

Contribution

It provides a gauge-independent Hamiltonian analysis and compares area-preserving and diffeomorphism-invariant theories in 1+1D quantum gravity.

Findings

The two theories are essentially equivalent despite differences.

The analysis confirms gauge independence and explores anomalous Ward identities.

Technical differences do not affect the core equivalence.

Abstract

We investigate the gauge-independent Hamiltonian formulation and the anomalous Ward identities of a matter-induced 1+1-dimensional gravity theory invariant under Weyl transformations and area-preserving diffeomorphisms, and compare the results to the ones for the conventional diffeomorphism-invariant theory. We find that, in spite of several technical differences encountered in the analysis, the two theories are essentially equivalent.