Let μg and μp denote the Gaussian and Poisson measures on R, respectively. We show that there exists a unique measure μ̃g on C such that under the Segal-Bargmann transform Sμg the space L (R, μg) is isomorphic to the space HL(C, μ̃g) of analytic L-functions on C with respect to μ̃g . We also introduce the Segal-Bargmann transform Sμp for the Poisson measure μp and prove the corresponding result. A...

Improvements are performed on a recently proposed statistical theory of the mean field of a many-fermion system. The dependence of the predictions of the theory upon its two basic ingredients, namely the Hartree-Fock energy and the average energy of the two particle–two hole excitations, is explored.

The matrix elements of local operators such as the electromagnetic current, the energy momentum tensor, angular momentum, and the moments of structure functions have exact representations in terms of light-cone Fock state wavefunctions of bound states such as hadrons. We illustrate all of these properties by giving explicit light-cone wavefunctions for the two-particle Fock state of the electro...

Canonical transformations are studied in the bosonic Fock space using coherent and ultracoherent vectors. The connection between the Weyl operator and the homogeneous canonical transformations (Bogoliubov transformations) is presented. The unitary ray representation of the symplectic group is defined in the bosonic Fock space by the action of the group on the ultracoherent vectors.

We consider some curious aspects of single-species free Fock spaces, such as novel bosonization and fermionization formulae and relations to various physical properties of bosonic particles. We comment on generalizations of these properties to physically more interesting many-species free Fock spaces.

Within the Hartree-Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the singleparticle energy at the Fermi momentum. It is shown that the Hartree-Fock result brings no corrections to the RPA Fermi velocity.

Spontaneous fission barriers, quadrupole inertia, and zero-point quadrupole-energy corrections are calculated for 252,256,258 Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing dynamical inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and crank-ing ansatz. The Skyrme results are compared with those of the ...

We construct the Fock space representation of quantum affine algebras using combinatorics of Young walls. We also show that the crystal basis of the Fock space representation can be realized as the abstract crystal consisting of proper Young walls. We then generalize Lascoux-Leclerc-Thibon algorithm to obtain an effective algorithm for constructing the global bases of basic representations.

Two restricted C[q, q]−forms of the well known q-boson algebra are introduced and the corresponding restricted q-Fock spaces defined. All of the irreducible highest weight representations, including the infinite dimensional ones, of U res ǫ (sl2) of type 1 are constructed through the restricted q-Fock spaces.

We investigate the expression of natural numbers in any base from a quantum point of view. In particular, resorting to the one-to-one correspondence between natural numbers and Fock states, we construct a set of multiboson operators and a set of translation operators, whose action on the Fock states leads to the coefficients identifying a natural number in any base.