CoreLumen Fundamental II : Quantum Field Theory of the Phase Vacuum

This work develops the quantum field theory of the phase sector of theCoreLumen vacuum condensate. Within the CoreLumen framework the physical vacuum is interpreted asa condensate medium described by the order parameter Ψ = ρ e^{iθ}. In CoreLumen Fundamental I the condensate structure was derived from amicroscopic complex scalar field undergoing spontaneous symmetry breaking.The broken phase naturally generates the condensate variables used in theCoreLumen vacuum framework. The present work focuses on the dynamics of the phase field θ and developsthe quantum field theory governing the phase sector of the condensate. The phase field carries a conserved Noether current Jμ = ρ² ∂μ θ which governs the coherent flow of the vacuum medium. The resulting low-energy effective theory describes the collectivephase dynamics of the condensate and provides the microscopic originof the vacuum dynamics used in the CoreLumen gravity and cosmologyseries. In this interpretation the vacuum behaves as a phase-coherent quantummedium whose collective dynamics organize the large-scale behavior ofspacetime. This document is released as a Zenodo archival version as part of theCoreLumen Fundamental Physics Series.