C*-Algebra and Mathematical Foundations of Quantum Statistical Mechanics

DATES: 28 and 31 March 2022 (4 sessions)
TIME: 10:00-12:00 and 14:30-16:30 (a total of 8 hours)
LOCATION: BCAM and Online

ABSTRACT:
In this course we aim at giving to non-experts the elementary mathematical bases of the theory of C*-algebras used in quantum statistical mechanics. This course can also be seen as an introduction to the algebraic formulation of quantum statistical mechanics, without (explicit) references to Hilbert spaces. We will in particular go from the finite-dimensional situation to the infinite-dimensional one via examples of fermions and quantum-spin algebras.

PREREQUISITES:
A good knowledge of elementary functional analysis

REFERENCES:
[1] Brattelli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechan-
ics, vols. I and II. 2nd ed. Springer. New York, 1996.
[2] B. Israel, Convexity in the theory of lattice gases. Princeton Series in Physics.
Princeton Univ. Press, 1979.
[3] J.-B. Bru and W. de Siqueira Pedra, C*-Algebra and Mathematical Foundations of Quantum Statistical Mechanics, in preparation.

*Registration is free, but mandatory before 21 March. To sign-up go to https://forms.gle/BiYNkHPrfRrhKHG38 and fill the registration form.

• BCAM-Course_20220328