On a2(1) reflection matrices and affine Toda theories

We construct new non-diagonal solutions to the boundary Yang-Baxter equation corresponding to a two-dimensional field theory with U_q(a₂⁽¹⁾) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary crossing symmetry are then used to find overall scalar factors which lead to consistent reflection matrices. Using the boundary bootstrap equations we also compute the reflection factors for scalar bound states (breathers). These breathers are expected to be identified with the fundamental quantum particles in a₂⁽¹⁾ affine Toda field theory and we therefore obtain a conjecture for the affine Toda reflection factors. We compare these factors with known classical results and discuss their duality properties and their connections with particular boundary conditions.     

Construction of coherent states for Morse potential: A su(2)-like approach

We propose a generalized su(2) algebra that perfectly describes the discrete energy part of the Morse potential. Then, we examine particular examples and the approach can be applied to any Morse oscillator and to practically any physical system whose spectrum is finite. Further, we construct the Klauder coherent state for Morse potential satisfying the resolution of identity with a positive measure, obtained through the solution of truncated Stieltjes moment problem. The time evolution of the uncertainty relation of the constructed coherent states is analyzed. The uncertainty relation is more localized for small values of radius of convergence.     

The classical su(2) invariance of the su(2) q -invariant XXZ spin chain

The XXZ spin-chain Hamiltonian has been constructed to be su(2) _q -invariant, but naively does not appear to be su(2)-invariant. However, using recently discovered deforming maps between representations of su(2) _q and corresponding representations of su(2), we prove a theorem which states that if a Hamiltonian is su(2) _q -invariant, it is also su(2)-invariant. The theorem generalizes to any quantized Lie algebra.     

Contraction of graded su(2) algebra

The Inönu-Wigner contraction scheme is extended to Lie superalgebras. The structure and representations of extended BRS algebra are obtained from contraction of the graded su(2) algebra. From cohomological consideration, we demonstrate that the graded su(2) algebra is the only superalgebra which, on contraction, yields the full BRS algebra.     

su q (2)-invariant harmonic oscillator

We propose a q-deformation of the su(2)-invariant Schrödinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but also to calculate the expectation values of some physically-relevant operators. Here we consider the case of the isotropic harmonic oscillator and of the quadrupole operator governing its interaction with an external field. We obtain the spectrum and wave functions both for q R⁺ and generic q S ¹, and study the effects of the q-value range and of the arbitrariness in the su _q (2) Casimir operator choice. We then show that the quadrupole operator in l = 0 states provides a good measure of the deformation influence on the wave functions and on the Hilbert space spanned by them.     

Classical and algebraic Hamiltonian with su(3) symmetry

We use Gelfand-Zetlin patterns to obtain the coherent state for an arbitrary symmetric irreducible representation of su(3). The semiclassical evolution of a dynamical system whose Hamiltonian contains the Casimir operators of both su(2) and so(3) subalgebras is investigated, and it is concluded that the presence of a common operator in the subalgebras induces integrability despite the absence of dynamical symmetry.     

THE WILSON LOOP EXPECTATION VALUES IN 2-AND 3-DIMENSIONAL su(2) LGT

An improved Monte Carlo scheme is applied to the computation of the expectation values of nxm Wilson loops in both 2-and 3-dimensional SU(2) lattice gauge theories.The results are compared with those simulated by the discrete group Y₁₂₀ and the exact results in two dimensions.     

Phase structure of SU(2) and SU(3) lattice gauge theories

Using a mean field we obtain the phase diagrams for SU(2) and SU(3) with a mixed fundamental-adjoint representation action.     

Calculation of the glueball mass spectrum ofSU (2) andSU (3) non-abelian lattice gauge theories II:SU (3)

We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0⁺⁺, 2⁺⁺, 0^?+ and, most interestingly from the experimental point of view, the oddball 1^?+. We calculate the 0⁺⁺ and 2⁺⁺ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature.     

Modular invariants for affine\widehat{SU}(3) theories at prime heights

A proof is given for the existence of two and only two modular invariant partition functions in affine theories at heightsn=k+3 which are prime numbers. Arithmetic properties of the ring of algebraic integers () which is related toSU(3) weights are extensively used.Chercheur IISN, Address after October 1: Dublin Institute for Advanced Studies, Dublin, IrelandChercheur IISN     

Quasi-periodic and Non-periodic Waves in (2+1)-Dimensional Nonlinear Systems

New exact quasi-periodic and non-periodic solutions for the (2 1)-dimensional nonlinear systems are studied by means of the multi-linear variable separation approach (MLVSA) and the Jacobi elliptic functions with the space-time-dependent modulus. Though the result is valid for all the MLVSA solvable models, it is explicitly shown for the long-wave and short-wave interaction model.     

Alternative scaling hypothesis forSU(2) andSU(3) lattice gauge theories

High precision data from a variety of sources forSU(2) andSU(3) Wilson action lattice gauge theory are analyzed with respect to the hypothesis of the possible existence of a zero temperature deconfining phase transition, in analogy with theU(1) theory. The internal energy, specific heat, string tension, and Wilson line, fit well to correlation length scaling laws associated with a finite order transition occurring at the weak coupling end of the crossover region for both theories. TheSU(2) theory is consistent with a correlation length exponent ν=2/3 and critical pointβ _c ≈2.47. ForSU(3) the data fit well to ν=1 andβ _c ≈6.69. Additional indirect evidence for the existence of such phase transitions is discussed, as is the possible crucial role of light dynamical fermions in the confinement mechanism.     

Charged states in ℤ2 gauge theories

Charged translation covariant states with finite energy are constructed in the Higgs phase of the ?₂ gauge theory coupled to a ?₂ matter field.     

The Baker-Campbell-Hausdorff formula for the chiral su(2) supergroup

In the theory of supersymmetricSU(2) Yang-Mills fields described on the 8th dimensional superspace, the local gauge transformations constitute a group whose Lie algebra has as coefficients belonging to the Weyl-spinorial Grassmann algebra.We present here a Baker-Campbell-Hausdorff formula for the chiralSU(2) supergroup and using this formula we give the finite form of each element of this group in terms of the local fields emering in the infinitesimal real superscalar generator.On leave at Departamento de Física, Universidad Simón Bolivar, Apartado 80659, Caracas 108 Venezuela     

ANALYTIC STUDY OF su(3) LATTICE GAUGE THEORY

The variational-cumulant expansion method has been extended to the case of lattice SU(3) Wilson model.The plaquette energy as an order parameter has calculated to the 2nd order expansion.No 1st order phase transition in the d=4 case is found which is in agreement with the monte Carlo results,and the 1st order phase transition in the d=5 case is clearly seen.The method can be used in the study of problems is LGT with SU(3) gauge group.