Linearized Quantum Gravity Using the Projection Operator Formalism

TL;DR

This paper applies the Projection Operator formalism to quantize linearized gravity without gauge fixing, revealing a unique constraint structure and confirming that physical states depend only on transverse-traceless modes.

Contribution

It introduces a gauge-independent quantization method for linearized gravity using the Projection Operator formalism, highlighting new features in the constraint algebra.

Findings

Constraint algebra becomes partially second-class after secondary constraints.

Physical Hilbert space depends only on transverse-traceless degrees of freedom.

No gauge or coordinate choices are needed in the quantization process.

Abstract

The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a flat background. As a result of the coordinate independence and linear truncation of the perturbation series, the constraint algebra surprisingly becomes partially second-class in both the classical and quantum pictures after all secondary constraints are considered. While new features emerge in the constraint structure, the end result is the same as previously reported: the (separable) physical Hilbert space still only depends on the transverse-traceless degrees of freedom.