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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 7: Quantum field theory
MP 7.6: Vortrag
Mittwoch, 23. März 2022, 18:25–18:45, MP-H5
A C*-algebraic approach to the classical limit of quantum systems — •Christiaan van de Ven1 and Valter Moretti2 — 1Max Planck Institute for Mathematics in the Sciences, Leipzig,Germany — 2Università di Trento, Trento, Italy
Quantization refers to the passage from a classical to a corresponding quantum theory. The converse problem, called the classical limit of quantum theories, is considered as a much more difficult issue and poses an important question for various areas of modern mathematical physics.
In this talk I will present this notion, first by introducing a natural framework based on the theory of deformation quantization. Subsequently, I will show that this setting is perfectly suitable to model the classical limit of quantum theories. More precisely, the corresponding quantization maps allow us to take the limit for ℏ→ 0 of a suitable sequence of algebraic states induced by ℏ-dependent eigenvectors of several quantum models, in which the sequence converges to a probability measure on the pertinent phase space.
In addition, since this C*-algebraic approach allows for both quantum and classical theories, it provides a convenient way to study the theoretical concept of spontaneous symmetry breaking (SSB) as an emergent phenomenon when passing from the quantum realm to the classical world by switching off the semi-classical parameter ℏ. This is illustrated for several physical models, e.g. Schrödinger operators and mean-field quantum spin systems.