Berlin 2024 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Quantum Field Theory II

MP 8.7: Talk

Wednesday, March 20, 2024, 12:00–12:20, HL 001

Extensions of Thermal States in Fermionic Systems — •Johannes Große and Gandalf Lechner — Department of Mathematics, FAU Erlangen-Nürnberg

The theory of C*-dynamical systems allows for a natural notion of thermal equilibrium state. An important question arising in this context is, whether a thermal state can be extended from a given observable algebra to a larger one. We show that, for a general C*-dynamical systems which enlarged by a Z2 action, the extensions are parametrized by dominated twisted thermal functionals. Applying the general theory to the CAR algebra yields a simple Gibbs type criterion, which directly answers the question of existence and uniqueness of extensions of the thermal state. The issue of extending thermal equilibrium states can be naturally framed in the language of Tomita-Takesaki modular theory and Z2 crossed products. This talk is based on [arXiv:2402.15574].

Keywords: algebraic quantum field theory; finite temperature; thermal states; Tomita-Takesaki modular theory; crossed products