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This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.

C*-algebras. --- Differentiable dynamical systems. --- Harmonic analysis. --- Operator theory. --- Functional analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Harmonic analysis

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Mathematical control systems --- Ordinary differential equations --- Differentiable dynamical systems --- Lyapunov exponents --- Stochastic systems --- Dynamique différentiable --- Systèmes stochastiques --- Congresses --- Congrès --- Congresses. --- 51 --- -Lyapunov exponents --- -Stochastic systems --- -Systems, Stochastic --- Stochastic processes --- System analysis --- Liapunov exponents --- Lyapunov characteristic exponents --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Mathematics --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Systems, Stochastic --- Dynamique différentiable --- Systèmes stochastiques --- Congrès --- Stochastic systems - Congresses. --- Lyapunov exponents - Congresses. --- Differentiable dynamical systems - Congresses.

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Ordinary differential equations --- Delay differential equations --- Differentiable dynamical systems --- Congresses. --- 51 --- -Differentiable dynamical systems --- -Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Delay equations (Differential equations) --- Delay functional differential equations --- Differential delay equations --- Differential equations with lag --- Functional differential equations --- Retarded argument (Differential equations) --- Retarded differential equations --- Retarded functional differential equations --- Time-lag systems (Differential equations) --- Mathematics --- Congresses --- Delay equations --- Retarded argument --- Time-lag equations --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Differential dynamical systems --- Delay differential equations - Congresses. --- Differentiable dynamical systems - Congresses.