Systematic isolation of the intensive scalar-field sector

Investigate whether the intensive definition of the Group Field Theory scalar-field operator proposed by Marchetti et al. provides a systematic way to isolate the physical sector of scalar-field expectation values.

Background

The scalar field reconstructed from the condensate phase is defined through an expectation value whose effective equation admits an extensive branch of solutions that scales with the cosmological volume. Because these solutions are regarded as physically inadmissible, the physically relevant configurations constitute only a subset of the full solution space.

An intensive definition of the Group Field Theory scalar-field operator has been proposed in prior work. The unresolved issue is whether that definition systematically removes the volume-scaling, unphysical sector and thereby isolates the physically meaningful scalar-field expectation values, both for the homogeneous field and in the related perturbative setting.