Scalar Field on a higher-spin Background via Fedosov quantization

TL;DR

This paper develops a covariant approach to scalar fields in higher-spin backgrounds using Fedosov quantization, connecting higher-spin gravity, phase space geometry, and quantum mechanics.

Contribution

It introduces a covariant formulation of scalar fields in higher-spin backgrounds via Fedosov quantization, unifying higher-spin gravity and quantum phase space methods.

Findings

Constructs a covariant action for scalar fields in higher-spin backgrounds.

Utilizes Fedosov quantization on the cotangent bundle.

Provides a framework for quantum mechanics on curved phase space.

Abstract

Conformal higher-spin gravity is the log-divergent part of the effective action of the scalar field coupled to background fields via higher-spin currents, as was defined by Segal and Tseytlin, which can be worked out over the flat space background. We revisit the problem of the scalar field in a higher-spin background and propose a manifestly covariant version thereof. The construction utilizes the Fedosov quantization of the cotangent bundle and the action is written with the help of the trace on a curved phase space that is provided by the Feigin--Felder--Shoikhet cocycle. The same construction allows one to formulate quantum mechanics on a curved space, the phase space being the cotangent bundle.