We prove several versions of the uncertainty principle for the Fock space F 2 in the complex plane. In particular, for any unit vector f in F , we show that dist (f ′ + zf, [f ]) dist (f ′ − zf, [f ]) ≥ 1, where [f ] = Cf is the one-dimensional subspace spanned by f . We also determine exactly when equality occurs above.

We perform continuous-choice Brueckner-Hartree-Fock calculations of hypernuclear matter, using the recent Nijmegen potentials for hyperon-nucleon and hyperon-hyperon interactions. Single-particle observables of the various hyperons in bulk matter, as well as properties of singleand double-lambda hypernuclei, employing an extended Skyrme-Hartree-Fock scheme, are presented. We find that the poten...

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We consider the nonlinear elliptic system ><>: −∆u+ u− u − βvu = 0 in B, −∆v + v − v − βuv = 0 in B, u, v > 0 in B, u = v = 0 on ∂B, where N ≤ 3 and B ⊂ R is the unit ball. We show that, for every β ≤ −1 and k ∈ N, the above problem admits a radially symmetric solution (uβ , vβ) such that uβ − vβ changes sign precisely k times in the radial variable. Furthermore, as β → −∞, after passing to a s...

We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree-Fock-like equation, which i...

A non-standard quantum deformation of the two-photon algebra h6 is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock–Bargmann realizations that provide a direct formalism for the definition of deformed states of light. Finally, the isomorphism between h6 and the (1+1) Schrödinger algebra i...

We discuss axially symmetric time-dependent Hartree-Fock calculations using a finite-range modification of the Skyrme energy functional. The finite-difference forms of the coordinate-space time-dependent Hartree-Fock equations, the method of time evolution, and other numerical aspects are presented. Detailed results for 84Krinduced deep-inelastic collisions with 208Pb at E 1,b = 494 MeV and wit...

Rotation-induced time-odd components in the nuclear mean field are analyzed using the Hartree-Fock cranking approach with effective interactions SIII, SkM*, and SkP. Identical dynamical moments J (2) are obtained for pairs of superdeformed bands 151 Tb(2)– 152 Dy(1) and 150 Gd(2)– 151 Tb(1). The corresponding relative alignments strongly depend on which time-odd mean-field terms are taken into ...

The Mickelsson-Faddeev (MF) algebra can naturally be embedded in a non-Lie algebra, which suggests that it has no Fock representations. The difficulties are due to the inhomogeneous term in the connection’s transformation law. Omitting this term yields a “classical MF algebra”, which has other abelian extensions that do possess Fock modules. I explicitly construct such modules and the intertwin...

We adress the problem of Fock space representations of (free) multiplet component fiels encountered in supersymmetric quantum field theory insisting on positivity and causality. We look in detail on the scalar and Majorana components of the chiral supersymmetric multiplet. Several Fock space representations are introduced. The last section contains a short application to the supersymmetric Epst...