In the work under review, the author surveys various applications of the Tomita-Takesaki theory in \({\mathcal O}^*\)-algebras [as presented in a homonymic paper by the same author, which is the first part of this work; see “Tomita-Takesaki theory in algebras of unbounded operators”, Lect. Notes Math. 1699 (1998; Zbl 0930.47042)] to quantum statistical mechanics and the Wightman quantum field theory.
The work is divided into four sections. In the first section unbounded CCR-algebras in finite degrees of freedom and dynamics of an interacting Boson model are discussed. The second section deals with standard systems in the BCS-Bogolubov model. Generalized standard systems are presented in the third section while the fourth one contains a discussion about standard systems in the Wightman quantum field theory.