Quantum algebras in phenomenological description of particle properties

Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to Lie algebras of the groups SU(n), taken for flavor symmetries of hadrons, in deriving new high-accuracy hadron mass sum rules, and (ii) the use of (multimode) q-oscillator algebras along with q-Bose gas picture in modelling the properties of the intercept \lambda of two-pion (two-kaon) correlations in heavy-ion collisions, as \lambda shows sizable observed deviation from the expected Bose-Einstein type behavior. The deformation parameter q is in case (i) argued and in case (ii) conjectured to be connected with the Cabibbo angle \theta_C.Comment: Latex, espcrc2.sty, 8 pages, 1 figure; v4: eq.(19) corrected. Based on talk given at the D.V.Volkov Memorial Conference (25-29 July, 2000, Kharkov, Ukraine

Entanglement in composite bosons realized by deformed oscillators

Composite bosons (or quasibosons), as recently proven, are realizable by deformed oscillators and due to that can be effectively treated as particles of nonstandard statistics (deformed bosons). This enables us to study quasiboson states and their inter-component entanglement aspects using the well developed formalism of deformed oscillators. We prove that the internal entanglement characteristics for single two-component quasiboson are determined completely by the parameter(s) of deformation. The bipartite entanglement characteristics are generalized and calculated for arbitrary multi-quasiboson (Fock, coherent etc.) states and expressed through deformation parameter.Comment: 5 pages; v2: abstract and introduction rewritten, references adde

Combined Analysis of Two- and Three-Particle Correlations in q,p-Bose Gas Model

q-deformed oscillators and the q-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept (''strength'') λ⁽²⁾ ≡ C⁽²⁾(K,K) - 1 of two-particle correlation function C⁽²⁾(p1,p2) of identical pions produced in heavy-ion collisions. Three- and n-particle correlation functions of pions (or kaons) encode more information on the nature of the emitting sources in such experiments. And so, the q-Bose gas model was further developed: the intercepts of n-th order correlators of q-bosons and the n-particle correlation intercepts within the q,p-Bose gas model have been obtained, the result useful for quantum optics, too. Here we present the combined analysis of two- and three-pion correlation intercepts for the q-Bose gas model and its q,p-extension, and confront with empirical data (from CERN SPS and STAR/RHIC) on pion correlations. Similar to explicit dependence of λ⁽²⁾ on mean momenta of particles (pions, kaons) found earlier, here we explore the peculiar behavior, versus mean momentum, of the 3-particle correlation intercept λ⁽³⁾(K). The whole approach implies complete chaoticity of sources, unlike other joint descriptions of two- and three-pion correlations using two phenomenological parameters (e.g., core-halo fraction plus partial coherence of sources)

On Chebyshev Polynomials and Torus Knots

In this work, we demonstrate that the q-numbers and their two-parameter generalization, the q,p -numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s, 2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q, p - numbers, the generalized two-variable Alexander polynomials and to prove their direct connection with the HOMFLY polynomials and the skein relation of the latter.У роботi показано, що q-числа та їх двопараметричнi узагальнення, q, p-числа можна використати для отримання деяких полiномiальних iнварiантiв торичних вузлiв i зачеплень. По-перше, показано, що q-числа, якi тiсно пов’язанi з полiномами Чебишова, можуть бути пов’язанi з полiномами Александера для класу T(s, 2) торичних вузлiв, де s – непарне цiле число, i використанi для знаходження вiдповiдного скейн-спiввiдношення. Потiм використано цю процедуру для отримання за допомогою q, p-чисел, двопараметричних узагальнених полiномiв Александера та показано зв’язок останнiх iз полiномiальними iнварiантами HOMFLY та їх скейн-спiввiдношенням

Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels

A scheme is proposed which allows to obtain special q-oscillator models whose characteristic feature consists in possessing two differing pairs of degenerate energy levels. The method uses the model of two-parameter deformed q,p-oscillators and proceeds via appropriately chosen particular relation between p and q. Different versions of quadratic relations p = f(q) are utilized for the case which implies two degenerate pairs E₁ = E₂ and E₃ = E₄. On the other hand, using one fixed quadratic relation, we obtain p-oscillators with other cases of two pairs of (pairwise) degenerate energy levels

Nonsingular multidimensional cosmologies without fine tuning

Exact cosmological solutions for effective actions in D dimensions inspired by the tree-level superstring action are studied. For a certain range of free parameters existing in the model, nonsingular bouncing solutions are found. Among them, of particular interest can be open hyperbolic models, in which, without any fine tuning, the internal scale factor and the dilaton field (connected with string coupling in string theories) tend to constant values at late times. A cosmological singularity is avoided due to nonminimal dilaton-gravity coupling and, for D > 11, due to pure imaginary nature of the dilaton, which conforms to currently discussed unification models. The existence of such and similar solutions supports the opinion that the Universe had never undergone a stage driven by full-scale quantum gravity.Comment: Latex 2e, 9 page

On centralizer algebras for spin representations

We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations