KMS states and complex multiplication

Kms States and the Chemical Potential for Disordered Systems

We extend the theory of the chemical potential associated to a compact separable gauge group to the case of disordered quantum systems. This is done in the natural framework of operator algebras. Among the other results, we show that the chemical potential does not depend on the disorder. The situation of the n–torus is treated in some detail. Indeed, provided that the zero– point is fixed inde...

Complex Multiplication

These are preliminary notes 1 for a modern account of the theory of complex multiplication. A shortened (minimal) version will be included in my book on Shimura varieties, and a complete longer version may one day be published separately. Please send comments and corrections to me at [email protected]. 1 This should be taken seriously: there are omissions, repetitions, clumsy statements and proof...

Complex Multiplication

Class field theory describes the abelian extensions of a number field using the arithmetic of that field. The Kronecker-Weber theorem states that all abelian extensions of the rationals are contained in cyclotomic fields. As we know, cyclotomic fields can be generated by special values of the exponential function e, and we call this the theory of complex multiplication for Gm. We would thus lik...

Perturbation Theory of W*-Dynamics, Liouvilleans and KMS-States

Kms States on the Square of White Noise Algebra

It was shown in [AFS00] that there are only three types of irreducible unitary representations θ of sl2. Using the Schurmann triple one can associate with each θ a number of representations of the square of white noise (SWN) algebra A. However, in analogy with the Boson, Fermion and q-deformed case, we expect that some interesting non irreducible representations of sl2 may result in GNS represe...