Broken algebra of currents and the Cabibbo angle

Hadron currents are introduced which violate the chiral SU(3) × SU(3) algebra, but leave the subalgebra of SU(2) × SU(2) unchanged. The coefficient of the symmetry breaking current can be related to the Cabibbo angle and the meson mass splitting. Two models are considered which give explicit values for this angle.     

Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

On the Boson Representations of SU(3) Algebra in the Basis SU(3)⊃U(1)+U(1)

The Dyson and Holstein-Primakoff boson realizations of the generators of SU(3) algebra have been given for the algebra chain SU(3)⊃U(1)+U(1), and a set of recursion formulae of the transformation matrix, which turn the Dyson onto the Holstein-. Primakoff representation, have been presented. The multiplicity that can occur in the reduction of SU(3)⊃U(1)+U(1) is naturally determined.     

The Unitarity of the W(3) Algebra from SU(3) Parafermion

We express the vacuum expectation value of the SU(3)k parafermion fields by that of two bosons and SU(3)_k current algebra. When k = 1,2,3, the SU(3)_k current algebra becomes an inner product of a unitary representation, and T(z), W⁽³⁾(z) are equivalent to "quasiself-adjoint" operators in this represen tation.     

Can the JPC = 1++ mesons form an ideal nonet?

In the framework of asymptotic SU(3) and the chiral SU(3) ? SU(3) charge algebra, it is argued that the 1⁺⁺ mesons can form an (almost) ideal nonet along with the 1^-- mesons. Experimental implications are also discussed.     

On a Lie group of infinite order as a nontrivial coupling of an intrinsic and space-time symmetries II

A real Lie algebra of denumerable infinite order that contains as subalgebras the Poincaré algebraP and the algebraSU(3) is derived by the method introduced in [1]. A nontrivial mass formula is obtained.     

SU(l|m|n)阶化代数及其规范模型

本文将阶化李代数SU(m|n)扩充到SU(l|m|n),并讨论了它的局部规范理论。找到了规范不变的拉格郎日量,并将SU(2|1)弱电模型推广到统一强、弱、电相互作用模型。 关键词：     

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．     

两参数变形量子代数SU(1,1)q,s的相干态及其性质

利用SU(1,1)_q,s量子代数的两参数变形振子构造出归一化的SU(1,1)_q,s相干态,证明了SU(1,1)_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(1,1)_q,s相干态的相干性受参数q、s的影响。     

Locally gauge-invariant formulation of parastatistics

A locally gauge-invariant formulation of parastatistics, which is equivalent to a Yang-Mills gauge theory, is given, using a complex Clifford algebra (case of SU(N)) or a real Clifford algebra (case of SO(N)). In particular, for the SU(3) case, the gauged theory of para-Fermi quarks is equivalent to quantum chromodynamics.     

Irreducible Representation of Quantum SLq(3) Algebra (Ⅰ)

The explicit forms of the irreducible representation matricea for the quantum SLq(3) enveloping algebra are computed in analogy to the irreducible tensor technique in the classical SU(3) algebra.     

On a relation between massive Yang-Mills theories and dual string models

The relations between mass terms in Yang-Mills theories, projective representations of the group of gauge transformations, boundary conditions on vector potentials and Schwinger terms in local charge algebra commutation relations are discussed. The commutation relations (with Schwinger terms) are similar to the current algebra commutation relations of the SU(N) extended dual string model.     

利用双参变形自旋相干态计算量子代数SU(2)q,s的Clebsch-Gordan系数

利用量子代数SU(2)_q,s的双参数变形自旋相干态,通过引入量子代数SU(2)_q,s的不可约表示张量积空间的Bargmann表示,导出了这一表示中不可约表示基底、双参数变形自旋相干态以及算符的表达式.最后导出了量子代数SU(2)_q,s在双参数变形自旋相干态下的Clebsch－Gordan系数.     

Departures from chiral symmetry

We review the physical concepts supporting the notion of an approximate hadron symmetry with special emphasis on the Nambu-Goldstone realizations of chiral SU (2) × SU (2) and SU (3) × SU (3). We stress the role of perturbation theory in the symmetry breaking as the technical instrument to connect broken symmetries with experiment. This is an alternate to the treatments that stress PCAC and current algebra. We find that chiral SU (2) × SU (2) is a good hadron symmetry to within 7% making it the best hadron symmetry after isotopic symmetry. The nonrenormalization theorem, Σ-terms, K_l3 decay, η→3π decay, the Goldberger-Treiman relation and many other specific processes and their relation to approximate chiral symmetry are discussed.     

Second class currents and broken SU(3)-symmetry

In the SU(3) limit, a second class, T-normal axial vector current, which transforms like an octet, can give rise to pseudotensor terms in the matrix elements for leptonic decays of baryons. With first order symmetry breaking, this second class current may generate pseudovector and pseudoscalar form factor contributions. It is an anti-hermitian current, but, even with SU(3) breaking, it does not need to disturb the chiral SU(2) × SU(2) algebra of charges.     

Unified Method for Dynamical Groups of Some Anharmonic Potentials

Realizations of the creation and annihilation operators for some important anharmonic potentials, such as the Morse potential, the modified Pöschl–Teller potential (MPT), the pseudoharmonic oscillator, and infinitely deep square-well potential, are presented by a factorization method. It is shown that the operators for the Morse potential and the MPT potential satisfy the commutation relations of an SU(2) algebra, but those of the pseudoharmonic oscillator and the infinitely deep square-well potential constitute an SU(1, 1) algebra. The matrix elements of some related operators are analytically obtained. The harmonic limits of the SU(2) operators for the Morse and MPT potentials are studied as the Weyl algebra.     

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

A new view of the virasoro algebra

It is shown that the local quantum field theory of the chiral energy-momentum tensor with central chargec = 1 coincides with the gauge invariant subtheory of the chiral SU(2) current algebra at level 1, where the gauge group is the global SU(2) symmetry. At higher level, the same scheme gives rise toW-algebra extensions of the Virasoro algebra.     

Current algebra Ward identities in the renormalized σ model

The many-current Ward identities corresponding to the Gell-Mann current algebra are discussed in the renormalized model. The Ward identities are verified in the case of the SU(2)×SU(2) chiral symmetry. In the SU(3)×SU(3) case the uniqueness of the Adler-Bardeen anomaly is proved using the Wess-Zumino consistency conditions.On leave of absence from the University of Genova (Italy).Chercheur Associé au C.N.R.S. (C.P.T./Marseille).     

A silicon bag model with SU(2) × SU(2) chiral dynamics

We describe a soliton bag model which incorporates explicitly SU(2) × SU(2) chiral dynamics, including the conservation of the polar vector current, the partial conservation of the axial vector current, and the SU(2) × SU(2) current algebra. This model appears to be renormalizable so that higher order effects may be treated systematically.