On the trace anomaly and the energy-momentum conservation of quantum fields at D=2 in classical curved backgrounds

TL;DR

This paper investigates the conformal anomaly and energy-momentum conservation for scalar fields in two-dimensional curved backgrounds, proposing a novel approach by splitting the scalar field to analyze quantum effects without including the metric determinant in the measure.

Contribution

It introduces a new method of splitting the scalar field to study anomalies and conservation laws without incorporating the metric determinant into the measure.

Findings

Reproduces known geometric quantities of the anomaly

Identifies additional terms involving the new field in the anomaly

Provides insights into quantum effects in 2D curved backgrounds

Abstract

We study the conformal symmetry and the energy-momentum conservation of scalar field interacting with a curved background at D=2. We avoid to incorporate the metric determinant into the measure of the scalar field to explain the conformal anomaly and the consequent energy-momentum conservation. Contrarily, we split the scalar field in two other fields, in such a way that just one of them can be quantized. We show that the same usual geometric quantities of the anomaly are obtained, which are accompanied by terms containing the new field of the theory.