Description
This monograph develops a unified framework - Signature Field Theory (SFT) - that reconceptualizes decision, cognition, and behavior as the dynamics of structured fields rather than evaluations of functions. Departing from classical models based on probability, utility, and separability, the theory introduces a complex field representation whose observable projection recovers probability as a derived quantity. Within this formulation, amplitude encodes intensity of preference, while phase encodes relational structure, context, and interference. The theory identifies intrinsic limits of inference (non-identifiability, gauge freedom, singularities) and extends the framework to multi-scale meta-fields, linking it to renormalization and hierarchical representations. The monograph demonstrates that classical probability theory, Cumulative Prospect Theory, and Quantum Cognition can be understood as limiting cases of the broader field framework. It further establishes formal correspondences with modern AI architectures, particularly transformer models, interpreting embeddings, attention, and layer structure as discrete approximations of continuous field dynamics. The central conclusion is that: By replacing functions with fields, optimization with dynamics, and static rationality with phase structure, CFT provides a unified theoretical foundation for analyzing decision processes across disciplines, from individual cognition to collective systems and artificial intelligence.