ON-LINE QLunch: Christiaan van de Ven

The concept of a 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). In this seminar we introduce the definitions, give several examples and show how quantization of the closed unit 3-ball $B^3\subset\mathbb{R}^3$ is related to quantization of its smooth boundary (i.e. the two-sphere $S^2\subset\mathbb{R}^3$). In the second part we apply this formalism to prove the existence of the 'classical limit' of quantum (spin) systems and discuss the concept of spontaneous symmetry breaking (SSB).