Quantum Sociodynamics for AI-Supported Sustainable City Transitions: A Gauge-Covariant Method for Modelling Symbolic Mediation and Public Trust

Quantum Sociodynamics (QSD) is introduced as a computational method for modelling symbolic influence and trust in artificial-intelligence-supported sustainable city transitions. Its central object, the Symbolic Mediation Field, represents how actor orientations, source–audience relations and communication histories shape signal effects. Actor states are encoded by complex variables ψi, symbolic transport by U(1) link variables Uij, signed coupling by qi and external interventions by Ji. Gauge-invariant measures capture local alignment, path transport and loop holonomy. Formal analysis establishes invariance under local re-description, path independence under zero holonomy and a classical DeGroot–Friedkin–Johnsen limit. Deterministic simulations demonstrate response reversal, order effects and persistent relational change after institutional shocks. A 27-record heat-pump corpus illustrates application to AI-assisted urban decarbonisation governance and identifies validation requirements.