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A. M. Gavrilik

Publications and source records attributed to A. M. Gavrilik.

63 records · Page 4Linked to original sources

q-Boson approach to multiparticle correlations

An approach is proposed enabling to effectively describe, for relativistic heavy-ion collisions, the observed deviation from unity of the intercept λ(measured value corresponding to zero relative momentum {\bf p} of two registered identical pions or kaons) of the two-particle correlation function C(p,K). The approach uses q-deformed oscillators and the related picture of ideal gas of q-bosons. In effect, the intercept λis connected with deformation parameter q. For a fixed value of q, the model predicts specific dependence of λon pair mean momentum {\bf K} so that, when |{\bf K}|\gsim 500 - 600 MeV/c for pions or when |{\bf K}|\gsim 700 - 800 MeV/c for kaons, the intercept λtends to a constant which is less than unity and determined by q. If q is fixed to be the same for pions and kaons, the intercepts λ_πand λ_K essentially differ at small mean momenta {\bf K}, but tend to be equal at {\bf K} large enough (|{\bf K}|\gsim 800MeV/c) where the effect of resonance decays can be neglected. We argue that it is of basic interest to check in the experiments on heavy ion collisions: (i) the exact shape of dependence λ= λ({\bf K}), and (ii) whether for |{\bf K}| \gsim 800 MeV/c the resulting λ_πand λ_K indeed coincide.

hep-ph↗

Masses of Decuplet Baryons Treated within Anyonic Realization of the q-Algebras U_q(su_N)

In the approach to hadronic flavour symmetries based on the q-algebras U_q(su_N) and proved to be realistic, the known construction of U_q(su_N) in terms of anyonic oscillators residing on 2d lattice is utilized. Anyonic Fock-like realization of basis state vectors is given for baryons (3/2)^+ from the 10-plet of U_q(su_3) embedded, via 20-plet of U_q(su_4), into the "dynamical" representation [4000] of U_q(su_5). Within the anyonic picture, we reobtain the universal q-deformed decuplet mass relation M_Ω-M_{Ξ^*}+M_{Σ^*}-M_Δ=[2]_q (M_{Ξ^*}-M_{Σ^*}), where [2]_q=q+q^{-1}=2 cosθ. Consistency with data for baryon masses requires θ\simeq\fracπ{14}. As a result, anyons with anyonic statistics parameter ν= 1/14 can be put into correspondence, at least formally, with the constituent quarks of decuplet baryons.

hep-ph↗

The Use of Quantum Algebras in Quantum Gravity

After a brief survey of the appearance of quantum algebras in diverse contexts of quantum gravity, we demonstrate that the particular deformed algebras, which arise within the approach of J.Nelson and T.Regge to 2+1 anti-de Sitter quantum gravity (for space surface of genus g) and which are basic for generating the algebras of independent quantum observables, are in fact isomorphic to the nonstandard q-deformed analogues U'_q(so_n) (introduced in 1991) of Lie algebras of the orthogonal groups SO(n), with n linked to g as n=2g+2.

gr-qc↗

Two-Particle Correlations from the q-Boson Viewpoint

We propose and develop to some extent a novel approach, which allows us to effectively describe, for relativistic heavy-ion collisions, the empirically observed deviation from unity of the intercept λ(i.e. the measured value corresponding to zero relative momentum {\bf p} of two registered identical pions or kaons) of the two-particle correlation function C(p,K). The approach is based on the use of two versions of the so-called q-deformed oscillators and the corresponding picture of ideal gases of q-bosons. By these techniques the intercept λis put into direct correspondence with the deformation parameter q. For fixed deformation strength, the model predicts dependence of the intercept λon the pion pair mean momentum {\bf K}.

nucl-th↗

q-deformed algebras $U_q(so_n)$ and their representations

For the nonstandard $q$-deformed algebras $U_q(so_n)$, defined recently in terms of trilinear relations for generating elements, most general finite dimensional irreducible representations directly corresponding to those of nondeformed algebras $so(n)$ (i.e., characterized by the same sets of only integers or only half-integers as in highest weights of the latter) are given explicitly in a $q$-analogue of Gel'fand-Tsetlin basis. Detailed proof, for $q$ not equal to a root of unity, that representation operators indeed satisfy relevant (trilinear) relations and define finite dimensional irreducible representations is presented. The results show perfect suitability of the Gel'fand-Tsetlin formalism concerning (nonstandard) $q$-deformation of $so(n)$.

q-alg↗

Quantum Groups in Hadron Phenomenology

We show that application of quantum unitary groups, in place of ordinary flavor SU(n_f), to such static aspects of hadron phenomenology as hadron masses and mass formulas is indeed fruitful. The so-called q-deformed mass formulas are given for octet baryons (1/2)^+ and decuplet baryons (3/2)^+, as well as for the case of vector mesons 1^- involving heavy flavors. For deformation parameter q, rigid fixation of values is used. New mass sum rules of remarkable accuracy are presented. As shown in decuplet case, the approach accounts for effects highly nonlinear in SU(3)-breaking. Topological implication (possible connection with knots) for singlet vector mesons and the relation q <---> θ_C (Cabibbo angle) in case of baryons are considered.

hep-ph↗

Multiparameter Deformations of the Algebra $gl_n$ in Terms of Anyonic Oscillators

Generators of multiparameter deformations $U_{q;s_1,s_2,...,s_{n-1}}(gl_n)$ of the universal enveloping algebra $U(gl_n)$ are realized bilinearly by means of appropriately generalized form of anyonic oscillators (AOs). This modification takes into account the parameters $s_1,...,s_{n-1}$ and yields usual AOs when all the $s_i$ are set equal to unity.

q-alg↗

Representations of the $U_q(u_{4,1})$ and a $q$-polynomial that determines baryon mass sum rules

With quantum groups $U_q(su_n)$ taken as classifying symmetries for hadrons of $n$ flavors, we calculate within irreducible representation $D^+_{12}(p-1,p-3,p-4;p,p-2)$ ($p \in {\bf Z}$) of 'dynamical' quantum group $U_q(u_{4,1})$ the masses of baryons ${1\over 2}^+$ that belong to ${\it 20}$-plet of $U_q(su_4)$. The obtained $q$-analog of mass relation (MR) for $U_q(su_3)$-octet contains unexpected mass-dependent term multiplied by the factor ${A_q\over B_q}$ where $A_q,$ $B_q$ are certain polynomials (resp. of 7-th and 6-th order) in the variable $q+q^{-1}\equiv [2]_q$. Both values $q=1$ and $q=e^{iπ\over 6}$ turn the polynomial $A_q$ into zero. But, while $q=1$ results in well-known Gell-Mann--Okubo (GMO) baryon MR, the second root of $A_q$ reduces the $q$-MR to some novel mass sum rule which has irrational coefficients and which holds, for empirical masses, even with better accuracy than GMO mass sum rule.

hep-ph↗