Quantum Geometry in Signature Space

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Description

This monograph develops a unified geometric framework for relativistic quantum physics by embedding gauge theories, gravitation, and quantum measurement within the General Theory of Signature Space (GTSS) and Cognitive Field Theory (CFT). Departing from function-based representations of physical systems, it advances a field ontology in which local laws, globalconsistency, and observational structure are integrated through the notion of closure. At the local level, gauge interactions are reinterpreted as Q-kernels, encoding differential sensitivity of fields under symmetry-constrained transformations. At the global level, gravitation and cosmological structure emerge as PTK potentials, ensuring compatibility among local responsesacross scales. This dual representation exposes a fundamental tension in modern physics: while gauge theories achieve local renormalizability, classical general relativity fails to close consistently at the quantum scale. This failure is recast as a problem of signature instability, rather than merely a technical divergence of perturbation series.

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