Square-lattice algebraic spin liquid with SO(5) symmetry

We propose a critical spin liquid ground state for S=1/2 antiferromagnets on the square lattice. In a renormalization group analysis of the "staggered flux" algebraic spin liquid, we examine perturbations, present in the antiferromagnet, which break its global SU(4) symmetry to SO(5). At physical parameter values, we find an instability towards a fixed point with SO(5) symmetry. We discuss the possibility that this fixed point describes a transition between the Néel and valence bond solid states, and the relationship to the SO(5) nonlinear sigma model of Tanaka and Hu.     

Non-periodic Ishibashi states: the su(2) and su(3) affine theories

We consider the su(2) and su(3) affine theories on a cylinder, from the point of view of their discrete internal symmetries. To this end, we adapt the usual treatment of boundary conditions leading to the Cardy equation to take the symmetry group into account. In this context, the role of the Ishibashi states from all (non-periodic) bulk sectors is emphasized. This formalism is then applied to the su(2) and su(3) models, for which we determine the action of the symmetry group on the boundary conditions, and we compute the twisted partition functions. Most if not all data relevant to the symmetry properties of a specific model are hidden in the graphs associated with its partition function, and their subgraphs. A synoptic table is provided that summarizes the many connections between the graphs and the symmetry data that are to be expected in general.     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie对称性 守恒量     

Classical and quantum Hamiltonian ratchets

We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and we derive a classical sum rule which allows one to predict the chaotic transport velocity from properties of regular phase-space components. Transport in quantum Hamiltonian ratchets arises by the same mechanism as long as uncertainty allows one to resolve the classical phase-space structure. We derive a quantum sum rule analogous to the classical one, based on the relation between quantum transport and band structure.     

Non-zero masses of π, K, η and κ mesons and algebraic realization of SU(3) × SU(3) chiral symmetry

An algebraic realization of SU(3) × SU(3) symmetry, with linearization on the SU(2) × Y subgroup taking into account masses of π, K, η mesons in virtual states is investigated. This is achieved by explicit breaking of the symmetry. The chosen form of the breaking term in the Lagrangian enables us to estimate the parameter c appearing in the squared mass operator. The obtained value of c(c ≈ ?1.17) is very close to that predicted by Gell-Mann, Oakes and Renner.     

A stability criterion for Hamiltonian systems with symmetry

We find a simple criterion for orbital stability for the general hamiltonian systems with symmetry in the equivariant symplectic and in the corresponding Poisson context.     

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.     

Lie symmetry, discrete symmetry and supersymmetry of the Pauli Hamiltonian

Starting from the full group of symmetries of a system we select a discrete subset of transformations which allows to introduce the Clifford algebra of operators generating new supercharges of extended supersymmetry. The system defined by the Pauli Hamiltonian is discussed. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001 Partially supported by the KBN-Grant # 5 P03B056 20.     

On a three-dimensional system with dynamical SU(3) symmetry

We show that a three-dimensional anisotropic oscillator in a magnetic field can display a dynamical SU(3) symmetry under certain conditions.     

U(3) and pseudo-U(3) symmetry of the relativistic harmonic oscillator

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.     

Dynamical rearrangement of SU(3) symmetry

The dynamical rearrangement of the SU(3) group is studied in connection with a 2-dimensional analogy of Holstein-Primakoff transformation. Infrared effect and low energy theorems are considered.     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

The representations and coupling coefficients of su(n); application to su(4)

Analytical expressions for the matrices and an explicit algorithm for computing Clebsch-Gordan coupling coefficients are given forsu(4) in au(3)-coupled basis as an example of the construction for anysu(n) in au(n−1) basis. The results areinduced from the known results foru(3) by means of the vector-coherent-state (VCS) theory of induced representations. The important recent result that makes this possible is the discovery that a complete set of shift tensors for the finitedimensional representations of reductive Lie algebras can be induced, by VCS methods, from those of suitably defined subalgebras.     

Confinement and the global SU(3) color symmetry

The global SU(3)color symmetry and its physical consequences are discussed.The Nother current is actually governed by the conserved matter current of color charges if the color field generated by this charge is properly polarized.The color field strength of a charge can have a uniform part due to the nontrivial QCD vacuum field and the nonzero gluon condensate,which implies that the self-energy of a system with a net color charge is infinite and,therefore,cannot exist as a free state.This is precisely what color confinement means.Accordingly,the Cornell type potential with the feature of Casimir scaling is derived for a color singlet system composed of a static color charge and an anti-charge.The uniform color field also implies that a hadron has a minimal size and minimal energy.Furthermore,the global S U(3)color symmetry requires that the minimal irreducible color singlet systems can only be qq,qqq,gg,ggg,qqg,qqqg,qqqg,etc.,therefore a multi-quark system can only exist as a molecular configuration if there are no other binding mechanisms.