Causal-Entropic Coherence Principle: A Spectral Criterion for UV-Finite Vacuum States in Quantum Field Theory

Abstract: Standard Quantum Field Theory (QFT), despite its phenomenological success, exhibits ultraviolet (UV) divergences that reveal a structural incompleteness. This work introduces the Causal-Entropic Coherence (CEC) Principle as a physical criterion for selecting admissible modal spectra in QFT. The CEC requires that the spectral coherence matrix of a quantum state satisfy: (i) causal support, (ii) finite spectral entropy, and (iii) subquadratic spectral growth. We show that the standard QFT vacuum violates these conditions, generating a "spectral contamination" responsible for UV divergences. To implement the CEC dynamically, we introduce a mediator field χ (x) that condenses infinite non-local constraints into a self-consistent local dynamics. As the main result, we obtain a finite vacuum energy scaling as EᵥacCEC ∼ M⁴, where M is the coherence scale, eliminating divergences without renormalisation. This principle establishes a bridge between horizon thermodynamics and the spectral structure of the vacuum, suggesting a basis for emergent gravity.