On the invariant distance and Green function for SU q(2)

Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU _q(2) the Green function on the q-Podler's sphere M _q = SU _q(2)/U(1) is derived. Possible applications are briefly discussed.     

Symmetries of SU(2) invariant Yang-Mills theories

It is shown that both the field equations and the self-duality equations of SU(2) invariant Yang-Mills theories do not allow any other Lie symmetries than those they have by construction, i.e., the 15 generators of the conformal group and the 3 generators of the gauge group. This is true in Euclidean as well in Minkowskian space-time.     

Indecomposable Representations of the Quantum Group SU(2)q1

The infinite-dimensional indecomposable representations are constructed by using the purely algebraic method and the matrix elements for these representations are obtained in an explicit form. Each familiar finite-dimensional irreducible representation ia induced on a quotient space.     

Two-Parameter Deformed Multimode Usui Operators of Multimode SU(2)q,s and SU(1,1)q,s Algebras

The two-parameter deformed (q,s-deformed)multimode Usui operators of multimodeSU(2)_q,s and SU(1,1)_q,s algebrasare introduced and the multimode q,s-Dyson bosonrealizations of both algebras are also given.     

利用SU（2）_（q，s）量子代数的两参数变形振子实现讨论SU（2）_（q，s）相干态

利用ＳＵ（２）ｑ，ｓ量子代数的两参数变形振子实现构造出与Ｐｅｒｅｌｏｍｏｖ相干态形式不同的ＳＵ（２）ｑ，ｓ相干态．证明了ＳＵ（２）ｑ，ｓ，量子代数的表示基是正交的，并讨论了它的相干态的归一性和完备性．指出ＳＵ（２）ｑ，ｓ相干态的相干性受参数ｑ，ｓ的影响，它比单参数变形ＳＵ（２）ｑ相干态更具一般性．     

An explicit description of the fundamental unitary for SU(2) q

In this paper we study the Cauchy problem for the generalized equation of finite-depth fluids

SU(2) q in a Hilbert space of analytic functions

The algebraSU(2) _q is realized in a Hilbert spaceH _q ² of analytic functions; the starting point is the differential realization of operators that satisfyq-algebra in a Hilbert spaceH _q. The Weyl realization ofSU(2) _q is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2×2 linear representation ofSU(2) _q is obtained as consistency conditions for couplingj1=j2=1/2 toj=0, 1; the derivation of Clebsch-Gordan coefficients is sketched and theq-generalization of the rotation matrices is included. The unitary correspondence ofH _q with a Hilbert space of complex functions of a real variable is also studied. The study presented in this paper follows Bargmann's formalism for the rotation group as closely as possible.     

Realizations of Multimode Quantum Group SU(2)q,s

By virtue of the concept of the two-parameterdeformed multimode bosonic oscillator, the Nodvik andHolstein–Primakoff realizations of thetwo-parameter deformed multimode quantum groupSU(2)_q,s are given. The deformed mappings between the multimodequantum group SU(2)_q,s and the two-parameterdeformed multimode bosonic oscillator are alsopresented.     

Meson-baryon scattering with SU (3) invariant interactions

The static model invariant under SU₃ is discussed. The baryons and mesons are assigned according to the “eightfold way”, and the Low equation for the scattering matrix is derived. The scattering matric has been diagonalized for arbitrary mixing ofF- andD-type coupling and the crossing matrix has been calculated. To determine the mixing of the two couplings photoproduction cross sections have been calculated. From the comparison of theK ⁺ Λ andK ⁺ Σ0 production cross sections with experiment it follows that α=D/F=3.5. For this value of α the model predicts the 3/2 decublet resonance in very good agreement with the experimental situation.     

SU q (2) covariant\hat R-matrices for reducible representations

We consider SU _q (2) covariant -matrices for the reducible3 1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known -matrices for SO _q (3) and SO _q (3, 1). Also, they are the three -matrices which can be constructed by using four different SU _q (2) doublets. Only two of the three -matrices allow a differential structure on the reducible four-dimensional quantum space.     

Noncommutative SU(N) and gauge invariant baryon operator

We propose a constraint on the noncommutative gauge theory with U(N) gauge group which gives rise to a noncommutative version of the SU(N) gauge group. The baryon operator is also constructed.     

SU(N) invariant non-linear σ models

Two series of SU(N) invariant non-linear σ models are constructed using exceptional orbits of the adjoint representation of SU(N). Each of these models possesses infinitely many local as well as non-local conserved charges.     

Poisson Boundary of the Dual of SU q (n)

We prove that for any non-trivial product-type action α of SU_q(n) (0<q<1) on an ITPFI factor N, the relative commutant is isomorphic to the algebra L^∞() of bounded measurable functions on the quantum flag manifold . This is equivalent to the computation of the Poisson boundary of the dual discrete quantum group . The proof relies on a connection between the Poisson integral and the Berezin transform. Our main technical result says that a sequence of Berezin transforms defined by a random walk on the dominant weights of SU(n) converges to the identity on the quantum flag manifold. Supported by JSPS. Partially supported by the Norwegian Research Council. Supported by the SUP-program of the Norwegian Research Council.     

Asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction

An asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction is constructed. The gauge coupling constants are taken equal (in the order of magnitude) to the electromagnetic one. The strong interaction and the quark confinement is provided for by a gluonic mechanism. Some physical consequence of the model are briefly discussed.     

Solution of the SU(N) massless thirring model

In the present work a method is proposed of constructing the eigenvectors and finding the quantum numbers of SU(N) symmetric massless theories with four-fermion interaction for an arbitrary value of N.     

Unitary representations of the quantum group SU q (1,1): Structure of the dual space ofU q (sl(2))

Real forms of the quantum universal enveloping algebraU _q (sl(2)) and a topological quantum group associated with this algebra are discussed.     

Monte Carlo analysis of gauge invariant two-point functions in an SU(2) Higgs model

New order parameters involving ratios of gauge invariant correlation functions for distinguishing different phases - confined/screened or free charges - in systems with lattice gauge fields coupled to matter fields have been proposed by Fredenhagen and Marcu and by Bricmont and Fröhlich. Our Monte Carlo analysis of those quantities for an SU(2) gauge field coupled to scalar matter fields in the fundamental representation supports the theoretically expected behaviour. Also a new mass parameter determining the exponential decay of two-point functions is observed.     

Quantum resonances of the kicked rotor and the SU(q) group

The quantum kicked rotor map is embedded into a continuous unitary transformation generated by a time-independent quasi Hamiltonian. In some vicinity of a quantum resonance of order q, we relate the problem to the regular motion along a circle in a (q(2)-1) component inhomogeneous "magnetic" field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance.