CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calcdlated and the influence of coset pure gauge fields of an abelian chiral group G=U₁×U₁⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion in lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current current propagator which has no influence on confinement properties of the system. When subgroup H is U_s, the coset puregauge fields have no influence on wnfinement properties of the system either.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct a lattice formulation of the pure gauge fields on a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a four-dimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the confinement properties of the quark system by calculating lattice current-current propagator when the coset pure gauge fields remain manifest.     

CONFINEMENT PROPERTIES OF PURE GAUGE FIELCS ON COSET SPACE OF THE NON-ABELIAN CHIRAL GROUP

In this paper the method of lattlce gauge theories is applied to the investigation of the effect of coset pure gauge fields of the non-Abelian chiral group on the confinement properties of a system. In particular, the current-current propagator of the coset G/H=SU(2)_L×(2)_r/SU(2) model is calculated. Then it IS found that the pure gauge fields-on coset space only offer a perimeter law factor which does not change the confinement properties of a physical system.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct the lattice formulation of the pure gauge fields in a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a fourdimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the quark system by calculating latt-ice current-current propagztor when the coset pure gauge fields are retained manifest1y.     

Center flux correlation in SU(2) Yang-Mills theory

By using the method of center projection, the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of nontrivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in the Landau gauge) in the low momentum regime and to give rise to a power-law correction proportional to p(-2.9(1)) at high momentum. The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase transition, which naturally explains the second order nature of this transition consistent with the vortex picture. Finally, the ghost propagator of the maximal center gauge is found to be infrared finite and, thus, shows that the coset fields play no role for confinement.     

Infrared gluon and ghost propagator exponents from lattice QCD

The compatibility of the pure power law infrared solution of QCD and lattice data for the gluon and ghost propagators in Landau gauge is discussed. For the gluon propagator, the lattice data are well described by a pure power law with an infrared exponent κ∼0.53, in the Dyson–Schwinger notation. κ is measured using a technique that suppresses finite volume effects. This value is consistent with a vanishing zero momentum gluon propagator, in agreement with the Gribov–Zwanziger confinement scenario. For the ghost propagator, the lattice data seem not to follow a pure power law, at least for the range of momenta accessed in our simulation.     

THE EVIDENCE OF DECONFINEMENT PHASE TRANSITION OF SU(2) LATTICE GAUGE MODEL BY MONTE CARLO METHOD

In this paper,we have calculated the SU(2) lattice gauge by the Monte Carlo method.For the finite temperature problem 8³×4 lattice is used and for the zero temperature problem 8⁴ lattice.From the calculations of the energy density,heat capacity and entropy density,the results indicate that there is a deconfinement phase transition when T/Λ_L=40—50.     

A VARIATIONAL METHOD IN LATTICE GAUGE THEORY BASED ON HÖLDER INTEGRAL INEQUALITY

A variational method based on Hölder integral inequality is presented. Taking the parameters in integral inequality as variational parameters, we can calculate the free energy in lattice gauge system. The plaquatte energy of Z₂ 、U(1)、 SU(2) gauge system is found and consistent with that given by Monte Carlo method. But, the higher phase transitions for U(1), SU(2) gauge systems are not found.     

THE ANALYTIC RESULTS FOR U1 AND SU2 AVERAGE PLAQUETTE TO THE THIRD ORDER APPROXIMATION IN THE CUMULANT EXPANSION

In the lattice gauge theory, by using cumulant expansion, we calculate the average plaquette for U₁ and SU₂ group up to the third order approximation in 4 and 5 dimensions analytically. Our results are consistent with MC data. We also discuss the application of cumulant expansion techneque in lattice theory.     

A位平均离子尺寸对六方RMnO3多铁化合物的结构和性能调控

实验研究了A位离子的化学内压对Hol-xDyMnO3(0≤x≤1)固溶体相结构物理性质的影响,发现掺杂稀土离子Dy3+所引起的内压力可使具有六方结构的HoMnO3向高压正交钙钛矿结构转变,形成六方相、六方相与高压正交相混相以及高压正交相3个区域.利用Rietveld方法,对Hol-xDyxMnO3的X射线衍射数据进行结...     

ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ)

The Hilbert space and the representation of the generators of Virasoro algebra for bosonic string under a holomorphic polarization are given in this paper,It is shown that the contre term of Virasoro algebra may be interpreted as curvature of a holomorphic vector bundle (holomorphic Fock bundle) on coset space G¹¹=G/H where G denotes the conformal transformation group and H the one-parameter subgroup generated by the generator L₀.The condition of the conformal anomaly cancellation may be expressed as the vanishing curvature of the bundle which is obtained by the product of the holomorphic Fock bundle and the holomorphic ghost vacuum bundle.The geometric interpretations of both classical and quantized BRST operators,ghost and antighost operators are also discussed.     

Flutter of Finite-Span Flexible Plates in Uniform Flow

The flutter instability and response of finite-span flexible plates in uniform flow are investigated experimentally. The effects of the plate aspect ratio on its dynamic responses are mainly analyzed. A hysteretic phenomenon is observed and can be described such that the plate flutters spontaneously as the flow velocity is greater than a critical value UC and the plate returns to its stable state as the flow velocity is slowly decreased to another critical one UD. We find that the aspect ratio has a greater effect on UC than on UD. The flutter frequency decreases and the amplitude increases with the increase in the flow velocity. When the flutter instability of the plate occurs, three typical flutter modes are identified and are associated with the aspect ratio and the flow velocity.     

THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT

The properties of fermion causal Green's function is discussed according to the theory of spectral representation. The definition of effective mass is established from the view point of field theory, and the approximate expression of S_F' (p) as |p²|«M² and the asymptotic formula of S_F' (p) as p²→+∞ is given. In terms of these result the problem of quark confinement is discussed. We find that: (ⅰ) Based on the theory of spectral re presentation the concept of relative confinement is allowed, and if renormalization effect is strong, the quarks can demonstrate definitely lighter effective mass when they are far away from the mass shell; (ⅱ) Based on the theory of spectral representation the concept of absolute confinement is unallowable, even the absolute confinement is taken as the limit of relative confinement. That is if the concept of absolute confinement is introduced, we must discard a part of elementary hypothesis of spectral representation theory.     

Mass Splittings of L=1 States of Quarkonium and Lorentz Structure of Long-rang Confinement Potential

The Lorentz nature of linear confinement potential of quarkantiquark pair is analyzed in the potential model by using the fine mass splittings of L=1 spin triplets in cc and bb systems.It is found that the linear confinement potential has a mixed nature of the Lorentz scalar and vector (0≤η≤29%,η=0 represents the pure Lonentz scalar).For the tentatively measured χ(1¹P₁) and γ(1¹P₁) meson masses,it is shown that the pure Lorentz scalar of the linear confinement potential is required to obtain the mass of the former meson,while the mixture of 79% Lorentz scalar and 21% Lorentz vector is required to explain the mass of the latter one.     

THE U(90) DYNAMICAL SYMMETRY IN LIGHT NUCLEI

In the IBM4,when s.d.g bosons are presented,the symmetry group of the system is U(90) In this paper,the group chain.U₉₀ U₁₅(sdg)×U₆(ST) SU₁₅(sdg)×U₆(ST) SU₅(sdg)× O₆(ST) SO₅(dg)×O₃(S)×O₃(T) O₃(dg)×O₃(S)×O₃(T) O₃(J)×O₃(T) is discussed,the reduction rules and the typical energy spectra are obtained.An example of a spectrum with this dynamical symmetry is found out,where the even-even nucleus ³⁴S and odd-odd nucleus ³⁴Cl are in one multiplet.     

UNIFIED ELECTRO-WEAK MODEL IN SU (3)

In this paper a unified electro-weak model for leptons based on the SU(3) gaugegroup is suggested by means of four kinds of realization for the generators of thegroup. For all low energy electro-weak processes, this model predicts the same resultsas the conventional Weinberg-Salam model does. The Weinberg angle is shown to be sin²θ_w=1/4 in a natural way. When the Higgs self potential respects a discrete symme-try Φ→-Φ, a new conserved quantum number called weak strangeness emerges fromthe model after spontaneous symmetry breaking. In the present model there existanother four heavy vector gauge bosons V^± and U^±± together with some heavyfermions and Higgs scalars, which have non vanishing weak strangeness quantumnumbers. These weak strange particles have no direct couplings with leptons. Theirexistence will not influence the low energy electro-weak processes. Nevertheless, theycan be produced in pairs in high energy collisions and the lightest of them should bestable if the conservation of weak strangeness is exact. The experimental implicationsand the possibility of violation of the conservation of weak strangeness are also dis-cussed.     

THE REGGE TRAJECTORY OF MESONS AND THE SU(4) MASS RELATIONS

A relativistic equation of motion of a two particle system under the constraints p_i²-m_i²-U(x²)=0.(i=1,2), where U(x²) is an infinite spherical square well poten-tial, is applied to the SU(4) quark model of mesons. A set of linear mass relations areobtained. Instead of the linear relation between J and M², the Regge trajectory ob-tained is a relation between p_nl² and M², where ζ_nlπ are zeros of the spherical Besselfunctions. The new trajectory seems more satisfactory than the former one.     

Lyapunov Bounds for Lattice Gauge Dynamics

We study the classical Hamiltonian dynamics of the Kogut–Susskind model for lattice gauge theories on a finite box in a d-dimensional integer lattice. The coupling constant for the plaquette interaction is denoted λ². When the gauge group is a real or a complex subgroup of a unitary matrix group U(N), N≥ 1, we show that the maximal Lyapunov exponent is bounded by , uniformly in the size of the lattice, the energy of the system as well as the order, N, of the gauge group. Received: 20 December 1997 / Accepted: 21 July 1998     

THE MASS GAP IN 2+1 DIMENSIONAL SU(3) LATTICE CAUGE THEORY

We present a variational calculation of C=+1 and C=－1 glueball masses in 2+1 dimensional SU(3) lattice gauge theory using a Hamiltonian in which the ground state is exactly known.In the range 0<1/g²≤6,we obtain good scaling behaviour am₊=36.1g² and am_－=5.98g².     

THE SPECTROSCOPY OF FOUR-BARYON SYSTEM

In this paper, using SU(6) symmetry theory four-baryon system is discussed and a method of analyzing experimental spectra is provided. Because of the gound states of _ΛΛ⁴H, _ΛΛ⁴He_{, Λ}⁴He and ⁴He are in the same I. R. of SU(6), on can derives masses for _ΛΛ⁴H, _ΛΛ⁴He from the experimental data of _Λ⁴H, _Λ⁴He, and ⁴He. Calculation shows that these J^π=0⁺ double Λ hypernuclei _ΛΛ⁴H, _ΛΛ⁴He are not likely bound states.