Simple construction ofSU(3) representations using theSU(2) projection technique

SU(3) representations for theSU(3) SU(2) chain are constructed in a new way usingSU(2) projection operators. TheSU(3) D-functions, presented in new parametrizations, are expressed in terms ofSU(2) D-functions and 6j-symbols.Valuable discussions with Dr. J. Niederle are gratefully acknowledged.     

Mass operator in theSU(3)-symmetric strong coupling theory with pseudoscalar mesons

In this paper theSU(3)-symmetric model of a static baryon octet source interacting with pseudoscalar meson octet fields by the coupling of Yukawa type is considered in the strong coupling limit. Using the result derived earlier that the isobaric states form the basis of the unitary irreducible representation of the dynamical group G=T ₂₄ [SU(3) SU(2)], the mass operator is specified by the kinetic part of the Hamiltonian as a particular element of the universal enveloping algebra of the symmetry groupSU(3) SU(2) acting in the space of isobaric states.     

Hierarchy of symmetry breakings and neutral currents in anSU(6) grand unification model

In anSU(6) grand unification model with eight quarks and eight leptons belonging to 15-plet and singlet representations, the symmetry is spontaneously broken by the sequenceSU(6)SU(3) ^c ×SU(2)×U(1)×U(1)SU(3) ^c ×U(1). Fror two cases of symmetry breakings the effective weak neutral current coupling constants are compared with experiment. For theSU(3) ^c ×SU(2)×U(1)×U(1)×SU(3) ^c ×U(1) symmetry breaking, the coupling constants reproduce the Weinberg-Salam model with a small correction term. Agreement with the experimental mean values is improved with the correction term. Parity violation in atomic physics is also discussed.     

One-loop divergences in chiral perturbation theory and right-invariant metrics onSU(3)

In the framework of chiral perturbation theory, we compute the one-loop divergences of the effective Lagrangian describing strong and non-leptonic weak interactions of pseudoscalar mesons. We use the background field method and the heat-kernel expansion, and underline the geometrical meaning of the different terms, showing how the right-invariance of the metrics onSU(3) allows to clarify and simplify the calculations. Our results are given in terms of a minimal set of independent counterterms, and shorten previous ones of the literature, in the particular case where the electromagnetic fild is the only external source which is considered. We also show that a geometrical construction of the effective Lagrangian at orderO(p ⁴) allows to derive some relations between thefinite parts of the coupling constants. These relations do not depend on the scale used to renormalize.     

The O(g) coefficient in the thermodynamic potential of hot SU(N) gauge theories and MQCD

The non-perturbative input necessary for the determination of the

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(g⁶) part of the weak coupling expansion of the free energy density for SU(2) and SU(3) gauge theories is estimated. Although the perturbative information completing the contribution to this order is missing, we give arguments that the magnetic fluctuations are dominated by screened elementary magnetic gluons.     

SUSY and GUT threshold effects in SUSYSU(5) models

We study consequences of the threshold effects of supersymmetric (SUSY) and superheavy (GUT) particles to the gauge coupling unification condition in two specific supersymmetricSU(5) models, the minimal model and the missing doublet model with natural doublet-triplet splitting. We present a consistent treatment of theSU(2)×U(1) breaking mass terms in the SUSY particle threshold effects, as well as that of the top quark threshold effect, which have been ignored in previous works. The GUT threshold effects are constrained by the proton decay experiments and by some theoretical consistency conditions, but they are strongly model dependent. For example, under a certain assumption for the SUSY particle masses, the minimal model favors a large (>1 TeV) SUSY breaking scale or a high _s(m _z )(<0.12), whereas=" the=" missing=" doublet=" model=" allows=" a=" low="><1 tev)=" susy=" breaking=" scale=" for=" 0.11=">_s(m _z )>0.13. The consequences of these two models in the proton decay experiments are also briefly discussed.     

On the lifetime of the kappa meson

The lifetime of a hypotheticalκ meson with low mass, introduced byGlashow andWeinberg in a model for simultaneous breaking ofSU(3) and chiral symmetry, is calculated. The coupling constant of theκ toKπ is obtained by assuming that the divergence of the strangeness changing vector current is dominated by theκ pole.     

Anharmonic corrections in constant-cutoff soliton model

We suggest a quantum stabilization method for theSU(2) -model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then derive the results for anharmonic corrections to the hyperon energy in the bound-state approach to theSU(3)-soliton model for the hyperons, withSU(3)-symmetry breaking. Thus we show that the anharmonic corrections give, as in the case of the complete Skyrme model, negative contributions to the hyperon energies and that they are of the same order of magnitude as those obtained using the complete Skyrme model for bound heavy-flavor two-meson systems in the case of cascade hyperons.     

High scale perturbative gauge coupling in R-parity conserving SUSY <Emphasis Type="Italic">SO</Emphasis>(10) with longer proton lifetime

It is well known that in single step breaking of R-parity conserving SUSY SO(10) that needs the Higgs representations , the GUT gauge coupling violates the perturbative constraint at mass scales a few times larger than the GUT scale. Therefore, if the SO(10) gauge coupling is to remain perturbative up to the Planck scale ( GeV), the scale M_U of the GUT symmetry breaking is to be bounded from below. The bound depends upon specific Higgs representations used for SO(10) symmetry breaking but, as we find, cannot be lower than $1.5 \times 10$¹⁷ GeV. In order to obtain such a high unification scale we propose a two-step SO(10) breaking through SU(2)_L $\times$ SU(2)_R $\times$ U(1)_B-L $\times$SU(3)_C ( ) intermediate gauge symmetry. We estimate the potential threshold and gravitational corrections to the gauge coupling running and show that they can make the picture of perturbative gauge coupling running consistent at least up to the Planck scale. We also show that when by the Higgs representations , gravitational corrections alone with negligible threshold effects may guarantee such perturbative gauge coupling. The lifetime of the proton is found to increase by nearly 6 orders over the present experimental limit for . For the proton decay mediated by a dim = 5 operator a wide range of lifetimes is possible, extending from the current experimental limit up to values 2-3 orders longer. Received: 1 July 2005, Revised: 21 August 2005, Published online: 11 October 2005     

Analysis of the static spherically symmetricSU(n)-Einstein-Yang-Mills equations

The singular boundary value problem that arises for the static spherically symmetricSU(n)-Einstein-Yang-Mills equations in the so-called magnetic case is analyzed. Among the possible actions ofSU(2) on aSU(n)-principal bundles over space-time there is one which appears to be the most natural. If one assumes that no electrostatic type component is present in the Yang-Mills fields and the gauge is suitably fixed a set ofn-1 second order and two first order differential equations is obtained forn-1 gauge potentials and two metric components as functions of the radial distance. This system generalizes the one for the casen=2 that leads to the discrete series of the Bartnick-Mckinnon and the corresponding black hole solutions. It is highly nonlinear and singular atr= and atr=0 or at the black hole horizon but it is known to admit at least one series of discrete solutions which are scaled versions of then=2 case. In this paper local existence and uniqueness of solutions near these singular points is established which turns out to be a nontrivial problem for generaln. Moreover, a number of new numerical soliton (i.e. globally regular) numerical solutions of theSU(3)-EYM equations are found that are not scaledn=2 solutions.     

AnSU(2)l ⊗SU(2)r symmetric Yukawa model in the symmetric phase

The lattice regularizedSU(2)l ?SU(2)r symmetric scalar fermion model with explicit mirror fermions is investigated in the phase with unbroken symmetry. In the present work numerical Monte Carlo calculations with dynamical fermions are performed on 4³·8 and 4³·16 lattices near the expected perturbative Gaussian fixed point. The bare Yukawa coupling of the mirror fermion is fixed at zero. Global symmetries of the model are discussed, and the numerical results are supported by lattice perturbation theory.     

Axial-vector symmetry breaking and the mass generation of the singlet pseudoscalar meson

The Fabri-Picasso formulation of the spontancous breaking of theSU _A (3) symmetry is applied to theU _A (1) symmetry. It is argued that the notion of the spontaneous breaking of theU _A (1) symmetry is different from that of theSU _A (3) symmetry. In contrast to the octet sector, absence of the massless Goldstone mode amounts to the existence of an exotic vacuum-like degenerated state.     

Bäcklund transformation for axially symmetricSU(N) Bogomolny equations

The generalization of Neugebauer's Bäcklund transformation is given for the axially symmetricSU (N) Bogomolny equations. An analogue of the Neugebauer-Kramer mapping is constructed for theSU (3) case.     

Nucleon-nucleon and hyperon-nucleon interactions in the quark model

The resonating group method is used to calculate the³S,¹S, and P wave phase shifts of the nucleon-nucleon interaction in the six-quark model. For large distances, the model is supplemented by , , , and -meson exchange. We show that for meson exchanges which mediate the long-range behaviour we can now use theSU ₃ flavour ratios of the meson-nucleon coupling constants even for the -nucleon coupling. For the -meson one had to use in the OBEP's an -N coupling twice to three times as large as predicted by theSU ³ flavour to describe the short-range repulsion. We also calculated the nucleon-hyperon interaction and described the NA-scattering in agreement with the data. The model is also applied to the study of the EMC effect.Supported by the Deutsche Forschungsgemeinschaft.Invited talk to the symposium Mesons and Light Nuclei IV, Bechyn, Czechoslovakia, September 5–10, 1988.I would like to thank Dr. Bräuer, Dr. Fernandez, Dr. Shimizu, and Dipl.-Phys. Straub, with whom I was working on the results reported above.     

On the symmetries of the Hubbard model: application to finite-size clusters

We evaluate the density of states of the Hubbard model at half filling on a four-site cluster with periodic boundary conditions. The results are obtained from an exact diagonalization study of the model, where theSU(2) symmetry, the Yang\(\widetilde{SU}(2)\) pseudospin symmetry and the translational invariance of the Hamiltonian are explicitly taken into account.     

SU(2,2¦N) · 〈N′〉 superunified theory

We establish a superspaceU for supergauge actions, a conformal supergroupSU(2,2¦N), and a conformal extendedSU(2,2¦N) supergravity theory. Using the Lagrangian Higgs evolution mechanism under the supergroupSU(2,2¦N) SU(N) acting on the superspaceU, we advance anSU(2,2¦N)SUN superunified theory of a superunited system, discuss the Lagrangian evolution of the superunified theory, and give the fiber bundle geometry of all the above mechanisms.     

A note about the t’Hooft ansatz for SU(N) real-time gauge theories

The t’Hooft ansatz, which reduces the classical Yang-Mills theory to the λϕ⁴ one, is under consideration. It is shown that, in the framework of this ansatz, the real-time classical solutions for the arbitrary SU(N) gauge group are obtained by embedding SU(2) × SU(2) into SU(N). It is argued that this group structure is the only possibility in the framework of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown. The text was submitted by the authors in English.     

Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

Saturation of QCD ward identities above theSU(L)⊗SU(L) chiral transition

We discuss an effective Lagrangian model in which theU (1) chiral symmetry is restored above theSU (L) SU (L) chiral phase transition (L being the number of light flavours) and the topological susceptibilityX _YM of the pure Yang-Mills theory drops to zero above the chiral transition. A new order parameter is introduced for theU(1) chiral symmetry and a new exotic particle becomes relevant at high temperatures.     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.