Micro-level Operators of Coherence Synchronisation: Goffman, Collins and a Non-Classical Formalisation of Everyday Interaction

This paper develops a mathematical and conceptual synthesis between Erving Goffman’s microsociology and formal physical-mathematical frameworks, specifically Quantum-like Formalism and Causal Set Theory (CST). We model social situations as Hilbert spaces, where Goffmanian frames act as projection operators ($P_{\text{frame}}$) and interaction rituals serve as coherence pumps that sustain social reality against decoherence. Using Lüders projection rules, we formalize the dynamics of social stigma and institutional constraint as state reductions and density matrix operations. Furthermore, by mapping interaction chains onto directed acyclic graphs (DAGs) in CST, we demonstrate how micro-level ritual interactions generate discrete spacetime-like causal structures at the macro-sociological level. This work provides a rigorous mathematical architecture for Goffman's qualitative insights, bridging the gap between micro-interactional dynamics and quantitative sociological modeling.