Chapter 8 : Statistical measurements in C∗-algebraic formulation

史郎 石川

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

8.1 Statistical measurements (C∗-algebraic formulation) 8.2 General statistical system (Example) 8.3 Bayes theorem in statistical MT 8.4 Kalman filter in noise 8.5 Information and entropy 8.6 Belief measurement theory (=BMT) 8.7 Appendix (Bertrand's paradox)

R. Shankar

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

9.1 Statistical measurements (W∗-algebraic formulation) 9.2 The relation among systems (Proclaimʷ∗2 in SMTʷ∗) 9.3 Quantum mechanics in B(L²(R)) 9.4 The method of moments 9.5 Principal components analysis in MT

John von Neumann

David Pierre Ruelle

The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications in mind. In Chapter 2 we study some questions related to the quantum statistical mechanics of spin systems, with particular attention to the time evolution of infinite systems. The basic reference for these two chapters is Bratteli-Robinson: Operator algebras and quantum statistical mechanics I, II. In Chapter 3 we discuss the nonequilibrium statistical mechanics of quantum spin systems, as it is currently being developped.