We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of “second order freeness” and interpret the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for second order freeness. By introducing cyclic Fock space, we also give an operator algebraic model fo...

We establish a twisted analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ and a virtual character of Γ we construct twisted vertex operators on the Fock space spanned by the super spin characters of the spin wreath products Γ ≀ S̃n of Γ and a double cover of the symmetric group Sn for all n. When Γ is a subgroup of SL2(C) with the McKay virt...

We study the renormalization problem for the Hartree–Fock approximation of the O(N)−invariant φ model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct renormalization properties of the effective field equations, including Renormalization–Group invariance with the one–loop beta function. These new Hartree–Fock dynamic...

The optimized effective potential equations for atoms have been solved by parametrizing the potential. The expansion is tailored to match the known asymptotic behaviour of the effective potential at both short and long distances. Both single configuration and multi-configuration trial wavefunctions are implemented. Applications to several atomic systems are presented, improving on previous work...

To clear up both algebraic and geometric structures for integrable systems derived from selfconsistent field theory, in particular, geometric aspect of the random-phase-approximation (RPA) equation is exhibited on the basis of the viewpoint of symmetry of the evolution equation. The RPA equation for an infinite-dimensional Grassmannian is constructed. c © 2002 MAIK “Nauka/Interperiodica”.

The renormalization of a gapless Φ-derivable Hartree–Fock approximation to the O(N)-symmetric λφ theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [1] in order to preserve all the desirable features of Φ-derivable DysonSchwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) whil...

The notion of slant Toeplitz operators Bφ and kth-order slant Toeplitz operators B φ on the Fock space is introduced and some of its properties are investigated. The Berezin transform of slant Toeplitz operator Bφ is also obtained. In addition, the commutativity of kth-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.

In this Letter we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to shed further light onto the combinatorics arising from algebraic and Fock space properties of boson operators. © 2006 Elsevier B.V. All rights reserved.

Measures corresponding to quadratic exponential families can be characterized in a number of ways. For example, the generating function for their orthogonal polynomials has a special form, their Laplace transforms satisfy differential equations, etc. To this list we add a representation on a modified symmetric Fock space. For most of the talk, we will concentrate on the non-commutative version ...

Superdeformed states in light N = Z nuclei are studied by means of the self-consistent cranking calculation (i.e., the P+QQ model based on the cranked Hartree-Fock-Bogoliubov method). Analyses are given for two typical cases of superdeformed bands in the A 40 mass region, that is, bands where backbending is absent (40Ca) or present (36Ar). Investigations are carried out particularly for the fol...