Mathematical Foundations of Quantum Information Field Theory (QIFT)

This working paper presents the Mathematical Foundations of Quantum Information Field Theory (QIFT), a novel theoretical framework that proposes quantum information—not spacetime or matter—as the fundamental substrate of physical reality. QIFT introduces the concept of infons, discrete quanta of relational information, whose coarse-grained distributions give rise to emergent spacetime geometry via an information-theoretic metric structure. This paper rigorously define infon graphs and derive a new class of emergent metrics using differential geometry, information geometry, and quantum Hilbert-space formalism. The QIFT action and resulting field equations are derived from a variational principle, linking infon density to Ricci curvature and dynamical evolution. Analytic stability conditions are explored, and a sample solution—the Quantum Metric Resonator (QMR)—is presented to demonstrate how engineered negative-energy configurations can yield measurable curvature gradients and non-Newtonian thrust. The paper lays out precise definitions, theorems, derivations, and sample applications, offering a comprehensive and self-contained foundation for further theoretical development, experimental design, and interdisciplinary collaboration. Keywords:Quantum Information, Infon, Emergent Spacetime, Differential Geometry, Information Geometry, Quantum Field Theory, Quantum Gravity, Negative Energy, Gravitational Propulsion, Quantum Metric Resonator (QMR), Hilbert Space, Fisher Information Metric