We employ the twistor approach to the construction of U(2) multi-instantons à la ’t Hooft on noncommutative R. The noncommutative deformation of the Corrigan-Fairlie-’t Hooft-Wilczek ansatz is derived. However, naively substituting into it the ’t Hooft-type solution is unsatisfactory because the resulting gauge field fails to be self-dual on a finite-dimensional subspace of the Fock space. We r...

A momentum-dependent mean field potential, suitable for application in the transport-model description of nucleus-nucleus collisions, is derived in a microscopic way. The derivation is based upon the Bonn meson-exchange model for the nucleon-nucleon interaction and the Dirac-Brueckner approach for nuclear matter. The properties of the microscopic mean field are examined and compared with phenom...

Cumulants of noncommutative random variables arising from Fock space constructions are considered. In particular, simplified calculations are given for several known examples on q-Fock spaces. In the second half of the paper we consider in detail the Fock states associated to characters of the infinite symmetric group recently constructed by Bożejko and Guta. We express moments of multidimensio...

On the level-1 Fock space modules of the algebra Uq(ŝln) we define a level-0 action U0 of the Uq(ŝln), and an action of an abelian algebra of conserved Hamiltonians commuting with the U0. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials. e-mail: takemura@kurim...

Nicolas Privault Abstract The aim of this note is to introduce a calculus on Fock space with its probabilistic interpretations, and to give a detailed presentation of the associated quantum Itô formula. Calcul sur l’espace de Fock et une formule d’Itô non-commutative anticipante Résumé Le but de cette note est d’introduire un calcul sur l’espace de Fock et de donner une présentation détaillée d...

A b s t r a c t . In [S], [KMS] the semi-infinite wedge construction of level 1 Uq(A (1)) Fock spaces and their decomposition into the tensor product of an irreducible Uq(A(1))-module and a bosonic Fock space were given. Here a general scheme for the wedge construction of q-deformed Fock spaces using the theory of perfect crystals is presented. Let Uq(fJ) be a quantum affine algebra. Let V be a...

We analyze in details a conditional measurement scheme based on linear optical components, feed-forward and homodyne detection. The scheme may be used to achieve two different tasks. On the one hand it allows the extraction of information with minimum disturbance about a set of coherent states. On the other hand, it represents a nondemolitive measurement scheme for the annihilation operator, i....