Persistence of the Raychaudhuri-constraint anomaly in the coupled null system

Determine whether the anomaly found in the quantization of the Raychaudhuri constraint persists, is modified, or becomes part of a larger anomalous constraint algebra when transverse dynamics, including the spin-one momentum and the Damour constraint, is incorporated.

Background

The paper constructs the classical kinematical Poisson structure for the complete null gravitational phase space, retaining the spin-zero, spin-one, and spin-two sectors before imposing the Raychaudhuri and Damour constraints. This structure is intended as the starting point for quantization.

Earlier work identified an anomaly in the quantization of the Raychaudhuri constraint, whereas the present analysis adds the spin-one momentum and the Damour constraint and thereby allows the coupled dynamics of multiple null generators to be studied. The authors explicitly leave unresolved whether the previously observed anomaly survives unchanged, is altered by transverse dynamics, or is absorbed into a broader anomalous constraint algebra. This question is therefore a concrete unresolved issue for the quantum theory developed from the phase space constructed in the paper.