A note on states of von Neumann algebras
The author proves that on a von Neumann albebra (possibly of uncountable cardinality) there exists a family of states having mutually orthogonal supports (projections) converging to the identity operator.
A spectral theory for order unit spaces
An algebraic view of distributions and operators
An infinite level atom coupled to a heat bath.
Axiomatique quantique et algèbres normées non associatives
-cross products and a generalized quantum mechanical -body problem.
C*-algebraic generalization of relative entropy and entropy
Canonical commutation relations and interacting Fock spaces
We introduce by means of reproducing kernel theory and decomposition in orthogonal polynomials canonical correspondences between an interacting Fock space a reproducing kernel Hilbert space and a square integrable functions space w.r.t. a cylindrical measure. Using this correspondences we investigate the structure of the infinite dimensional canonical commutation relations. In particular we construct test functions spaces, distributions spaces and a quantization map which generalized the work of...
Chaotic decompositions in -graded quantum stochastic calculus
A brief introduction to -graded quantum stochastic calculus is given. By inducing a superalgebraic structure on the space of iterated integrals and using the heuristic classical relation df(Λ) = f(Λ + dΛ) - f(Λ) we provide an explicit formula for chaotic expansions of polynomials of the integrator processes of -graded quantum stochastic calculus.
Charged fields, Higgs phenomenon and confinement. Lesson from soluble models
Cocycle condition for multi-pullbacks of algebras
Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorphism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks...
Commuting normal operators in partial -algebras
Concerning the condition of additivity in quantum field theory
Construction of vacuum for the positive-energy representation and its Bose counterpart.
Decay of spatial correlations in thermal states
Distance between states and statistical inference in quantum theory
Entropy estimates for finitely correlated states
Exotic infrared representations of interacting systems
Extension techniques in -cross products by compact group duals and in quantum field theory.
Hall's transformation via quantum stochastic calculus
It is well known that Hall's transformation factorizes into a composition of two isometric maps to and from a certain completion of the dual of the universal enveloping algebra of the Lie algebra of the initial Lie group. In this paper this fact will be demonstrated by exhibiting each of the maps in turn as the composition of two isometries. For the first map we use classical stochastic calculus, and in particular a stochastic analogue of the Dyson perturbation expansion. For the second map we make...