Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) sub-structure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.Comment: 28 pages, LaTeX 12pt article styl

Deformations of the Boson sp(4,R)sp(4,R) Representation and its Subalgebras

The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space. One of the deformed representation is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and three representations of the noncompact u(1,1) are also deformed and are contained in this deformed algebra. They are reducible in the action spaces of sp(4,R) and decompose into irreducible representations. The other deformed representation, is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the standard deformed su(2). All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, an other deformation of su(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation is reducible and decomposes into irreducible ones that yields a complete description of the same

Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications

A multi-shell generalization of a fermion representation of the q-deformed compact symplectic sp_q(4) algebra is introduced. An analytic form for the action of two or more generators of the Sp_q(4) symmetry on the basis states is determined and the result used to derive formulae for the overlap between number preserving states as well as for matrix elements of a model Hamiltonian. A second-order operator in the generators of Sp_q(4) is identified that is diagonal in the basis set and that reduces to the Casimir invariant of the sp(4) algebra in the non-deformed limit of the theory. The results can be used in nuclear structure applications to calculate beta-decay transition probabilities and to provide for a description of pairing and higher-order interactions in systems with nucleons occupying more than a single-j orbital.Comment: 10 page

Coherent pairing states for the Hubbard model

We consider the Hubbard model and its extensions on bipartite lattices. We define a dynamical group based on the $\eta$-pairing operators introduced by C.N.Yang, and define coherent pairing states, which are combinations of eigenfunctions of $\eta$-operators. These states permit exact calculations of numerous physical properties of the system, including energy, various fluctuations and correlation functions, including pairing ODLRO to all orders. This approach is complementary to BCS, in that these are superconducting coherent states associated with the exact model, although they are not eigenstates of the Hamiltonian.Comment: 5 pages, RevTe

Challenges to support edge-as-a-service

A new era in telecommunications is emerging. Virtualized networking functions and resources will offer network operators a way to shift the balance of expenditure from capital to operational, opening up networks to new and innovative services. This article introduces the concept of edge as a service (EaaS), a means of harnessing the flexibility of virtualized network functions and resources to enable network operators to break the tightly coupled relationship they have with their infrastructure and enable more effective ways of generating revenue. To achieve this vision, we envisage a virtualized service access interface that can be used to programmatically alter access network functions and resources available to service providers in an elastic fashion. EaaS has many technically and economically difficult challenges that must be addressed before it can become a reality; the main challenges are summarized in this article

Quantitative SPECT/CT parameters of myocardial 99mTechnetium-3,3-diphosphono-1,2-propanodicarboxylic acid (DPD) uptake in suspected cardiac transthyretin amyloidosis

Background: 99mTc-labelled bisphosphonates are used for imaging assessment of patients with transthyretin cardiac amyloidosis (ATTR). Present study evaluates whether quantitative SPECT/CT measurement of absolute myocardial 99mTc-labelled 3,3-diphosphono-1,2-propanodicarboxylic acid (Tc-DPD) uptake can diagnose patients with suspected ATTR. / Methods: Twenty-eight patients (25 male, age 80.03 ± 6.99 years) with suspected ATTR referred for Tc-DPD imaging had planar and SPECT/CT imaging of the chest. Three operators independently obtained Tc-DPD myocardial SUVmax and SUVmean above threshold (SMaT) (20, 40 and 60% of SUVmax), using a semi-automated threshold segmentation method. Results were compared to visual grading (0–3) of cardiac uptake. / Results: Twenty-two patients (78%) had cardiac uptake (2 grade 1, 15 grade 2, 5 grade 3). SUVmax and SMaT segmentation thresholds enabled separating grades 2/3 from 0/1 with excellent inter- and intra-reader correlation. Cut-off values 6.0, 2.5, 3 and 4 for SUVmax, SMaT20,40,60, respectively, separated between grades 2/3 and 0 /1 with PPV and NPV of 100%. SMaT20,40,60(cardiac)/SUVmean (liver) and SMaT20,40,60(cardiac)/SUVmean(liver/lung) separated grades 2 and 3. / Conclusion: Quantitative SPECT/CT parameters of cardiac Tc-DPD uptake are robust, enabling separation of patients with grades 2 and 3 cardiac uptake from grades 0 and 1. Larger patient cohorts will determine the incremental value of SPECT/CT quantification for ATTR management

Small oscillations of a chiral Gross-Neveu system

We study the small oscillations regime (RPA approximation) of the time-dependent mean-field equations, obtained in a previous work, which describe the time evolution of one-body dynamical variables of a uniform Chiral Gross-Neveu system. In this approximation we obtain an analytical solution for the time evolution of the one-body dynamical variables. The two-fermion physics can be explored through this solution. The condition for the existence of bound states is examined.Comment: 21pages, Latex, 1postscript figur

On the use of the group SO(4,2) in atomic and molecular physics

In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.Comment: 31 page