Quantum spin systems and applications to hypergraphs

The concept of strict deformation quantization provides a mathematical formalism that describes the transition from a classical theory to a quantum theory in terms of deformations of (commutative) Poisson algebras (representing the classical theory) into non-commutative C*-algebras (characterizing the quantum theory). This theory is particularly suitable to model quantum spin systems in the ' classical' limit. In this seminar we introduce the basic ideas, provide several examples and finally propose possible generalizations to hypergraph theory.