Asymptotic equivalence of two strict deformation quantizations and applications to the classical limit

Abstract: 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). 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 $S^2 \subset \mathbb{R}^3$.) We will moreover give an application regarding the classical limit of a quantum (spin) system and discuss the concept of spontaneous symmetry breaking (SSB).

mathematical physicsdifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Deformation Quantization Seminar