Mini-course 

on modular theory in Statistical Mechanics and relativistic Quantum Field Theory

On October 17-18 we are organizing a mini-course on modular theory in Utrecht.

It takes place at Heidelberglaan 3 (in the University Library on the science campus), in Buchelius room 6.18

The idea is to present a modern mathematical point of view on entropy production in Statistical Mechanics and entanglement entropy in QFT, including an introduction to Tomita-Takesaki modular theory.

The mini-course is preceded by a reading seminar in Nijmegen taking place on Wednesday afternoons until mid October, see here for more details!

Schedule:

17 October 2024

12:30 - 14:30  |  Vojkan Jakšic (McGill University, Montréal)

  entropy and modular theory (finite systems), two-times measurements

15:00 - 16:00  |  Michał Wrochna (Utrecht University)

  quasi-free states and Araki-Woods representation

18 October 2024

10:30 - 12:30 &  13:30 - 14:30 |  Vojkan Jakšic (McGill University, Montréal)

  thermodynamic limit, modular theory in general setting, non-equilibrium statistical mechanics

15:00 - 16:00  |  Michał Wrochna (Utrecht University)

  relativistic quantum fields and Bisognano-Wichmann theorem

References:

V. Jakšic, slides (preliminary version) & M. Wrochna, slides 1, slides 2

V. Jakšic, Modular Theory: How and Why (lecture notes/slides, see IHP lecture, Paris 2024, cf. Göttingen 2016)
V. Jakšic, Y. Ogata, Y. Pautrat, C.-A. Pillet, Entropic fluctuations in quantum statistical
mechanics. An introduction. In: Quantum Theory from Small to Large Scales: Lecture Notes
of the Les Houches Summer School: Volume 95, August 2010 , Oxford University Press, USA
(2012), 213-410
V. Jakšic, Y. Ogata, C.-A. Pillet, R. Seiringer, Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
J. Derezinski, C. Gérard, Mathematics of Quantization and Quantum Fields
C. Gérard, Microlocal Analysis of Quantum Fields on Curved Spacetimes
S. Hollands, K. Sanders, Entanglement Measures and Their Properties in Quantum Field Theory
R. Brunetti, D. Guido, R. Longo, Modular localization and Wigner particles

see also videos of lectures by Huzihiro Araki: link 1, link 2.