Potential-moving,Migdal's recursion formula,differential renormalization and duality

Migdal's original recursion formula is rederived as a low-temperature approximation by an isotropic type of potential-moving. For self-dual spin or gauge systems this transformation is shown to be differentiably conjugate to another one, which is obtained as a high-temperature approximation. The conjugation relation is established through the duality mapping.This explains the mechanism leading to some exact results obtained with Migdal's differential renormalization equation. The last equation is also explicitly rederived as the result of potential-moving approximations inspired by the methods of differential renormalization in real space.Some applications and extensions of the above results are finally considered in connection with an approach, which was recently proposed for systematically improving Migdal's approximation.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

Covariant supermultiplet theory,the Zweig rule and the ψ particles

By interpreting duality diagrams as contractions over covariant SU(8) fields one obtains an ‘explanation’ of the Zweig rules and arrives at quantitative estimates for nonzero diagrams involving ψ's which do not disagree with experiment.     

Some solutions for Yang's equations for self-dual SU(2) gauge fields

It is shown that a large class of solutions of Yang's equations for self-dual SU(2) gauge fields can be obtained from the solutions of two-dimensional and four-dimensional Laplace equations.     

Supersymmetry and central charges

Superfield representations of supersymmetry algebras with central charges are studied. An interacting field theory realization of the SU(2) invariant example is given, which is shown to be just another interpretation of P. Fayet's “hypersymmetry”. For certain massless cases it is shown that the theory has a larger SU(4) invariance once the equations of motion are used, thus providing us with a possible superfield formulation of the SU(4) supersymmetric gauge theory.     

Superposition de deux ondes d'indices d'heterogeneite differents

Heterogeneous plane and uniform electromagnetic waves are particular solutions of Maxwell's equations. The sum of two of these solutions of the same frequency is generally not a wave of the same kind. A new type of interference appears for two heterogeneous plane and uniform components of different heterogeneity. The experimental proof of this phenomenon would show the dependence of the phase velocity on the heterogeneity. In the general case, the equal-amplitude surfaces of the various fields components are different; the same holds for the equal-phase surfaces. It is not always possible to define an eikonal and a wave surface for such a solution of Maxwell's equations. These difficulties disappear for waves of equal or opposite heterogeneity index.     

基于SU(3)对称性的27重态研究

奇特重子属于味SU(3)的高维表示, 可以通过研究与其属于同一多重态的非奇特伴子来了解其性质. 本文研究了PDG粒子数据表中可能的27重态. 通过经典SU(3)方法所采用的质量拟合和两体强衰变部分宽度的计算预言出具有不同宇称的两套27重态. 质量谱的拟合预言了新的非奇特态Λ(1780), 其他非奇特伴子都能在PDG中找到候选者; 衰变宽度的计算结果表明存在近似味SU(3)对称性. 进一步分析和对比其他理论模型的研究结果可以支持27重态指定的合理性.     

Research of SU(3) 27-plet

Exotics belong to high multiplet of SU(3), so one can understand them by researching their non-exotic partners in the same multiplet. Here the possible 27-plet from flavor SU(3) symmetry are investigated. By fitting the mass spectrum and calculating the two-body partial hadronic decay widths of members, two set of 27-plet baryons with different parities are found. For the mass spectrum, all non-exotic members have their candidates in PDG except for a new Λ(1780). For the decay widths, the computing results show the approximate flavor SU(3) symmetry. The further analyzing and comparing with the results from other theoretical models can support the rationality of the 27-plet assignment.     

New selection rules and symmetry relations for Regge-Regge cuts

Using SU(3) and duality constraints, Worden has shown that the Finkelstein cut selection rule requires that all odd signature Regge-Regge cuts are strongly suppressed in meson-baryon scattering. We have extended Worden's analysis by constructing the SU(3) coefficients, for the Gribov vertices, that are appropriate for dual resonance models. By combining the coefficients for two Gribov vertices and preserving the Finkelstein rule, a complete set of symmetry relations is obtained. Examples of these relations are that Regge-Regge cuts do not contribute to meson-meson scattering when the external mesons have overall odd C parity, and that the I = 2 part of Δ photoproduction cannot arise from Regge-Regge cuts.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

Contribution of meron-like configurations to 't Hooft's disorder parameter

t' Hooft's disorder parameter is written as a Euclidean functional integral over fields with singular boundary conditions. Meron-like configurations are constructed and their contributions to the disorder parameter is evaluated approximately. The calculated disorder parameter exhibits a confinement phase behaviour.     

Composite symmetries and sub-constituent models

Assuming the internal A-spin, B-spin and C-spin of particles from basic symmetry SO(4), the color SU(3), horizontal SU(3)', electroweak SU(2)'_w×U(1) and other higher composite symmetries are derived.     

Monte Carlo calculation of SU(2) glueball states with Manton's action

Using Manton's action we carry out a Monte Carlo variational calculation of the SU(2) glueball spectrum. We find a scaling window for the 0⁺ state, but no scaling for 1^?, 2⁺, 2^? and 3⁺ states. The 0⁺ result is consistent with universality.     

Accroissement d'energie interne et de densite d'energie interne d'un milieu dielectrique polarise

For an isotropic dielectric medium, having an arbitrary shape and a stationary polarization, the polarization-induced increase of internal energy of the dielectric only is reexamined from Güntelberg's thermodynamic point of view. The value obtained for this increase is quite different from what was previously admitted, even in the case of dielectrics with simple shapes. The new value is in better agreement with earlier results. It is furthermore well in accord with the exact macroscopic relation between the internal energy and a density of internal energy, a relation which is more intricate than the simple relation of integration largely accepted up to now.     

Explicit non-'t Hooft rational solutions of the Atiyah-Drinfeld-Hitchin-Manin instanton matrix equations for SU(2r)

The Atiyah-Drinfeld-Hitchin-Manin instanton matrix equations may be written as a pair, one quadratic and one linear. The explicit general solution of the quadratic equation is given in terms of rational functions of free parameters, thus reducing the ADHM equations to a single equation. For SU(2r), large families of explicit solutions, rational in free parameters, are constructed by this method. These new families are generally about twice as large as the previously known 't Hooft families, and contain non-'t Hooft solutions for every r ? 1.     

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 static and kinetic methods of conservative system stability,and Rayleigh's principle: A reexamination

The relation between the static and kinetic variational methods of the stability of equilibrium analysis of conservative systems and the corresponding static and kinetic Rayleigh's principles is reexamined. Specifically made explicit are the connections between (i) the virtual work principle (for the adjacent equilibrium configuration) and Rayleigh's principle of extremum critical loads and buckled modes, and (ii) Hamilton's principle (for the adjacent non-equilibrium configuration) and Rayleigh's principle of extremum frequencies and mode shapes, through simple familiar examples. These connections are found by considering, in addition to the familiar mode amplitude variations, variations of the load which in turn produce variations in the space (i) and time (ii) domain lengths, respectively; one is thus led to a variable endpoints variational problem (instead of the customary fixed endpoints one) which, by invoking the energetics of these adjacent configurations, is simplified and finally brought to the standard Rayleigh's principle form.     

Wehrl-Lieb's inequality for entropy and the uncertainty relation

Wehrl has defined a new classical entropy by means of coherent states and conjectured that this entropy is greater than one. Lieb proved Wehrl's conjecture. In our note we discuss a certain reformulation of the classical entropy. We show that Wehrl's inequality for reformulated entropy implies the usual version of the Heisenberg uncertainty relation.     

Weyl's association,Wigner's function and affine geometry

According to Weyl one may associate a function with a dynamical operator; these functions depend on the parameters p and q and can be displayed in a p, q manifold, the W space. In the classical limit the W space becomes the phase space parametrised by the canonical variables. The function associated in this manner with the density operator is Wigner's function. It turns out that if Wigner's function is a delta function it cannot represent the density operator of a physically realisable state unless the argument of the delta-function is linear in the parameters a and q. In all other cases Wigner's function associated with a physically realisable state has a finite width, proportional to $\text{h}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Consequently straightness (linear combination of p and q) has a fundamental significance in the W space. Since this property is preserved under linear inhomogeneous transformations the W space will have a geometry generated by these transformations, the affine geometry of Euler, Moebius and Blaschke. In the present note we show how this comes about, how it simplifies the semiclassical approximations of Wigner's function, and makes one understand how in the classical limit this geometry is lost, allowing to be replaced by the geometry of canonical transformations.     

Comments on the derivation of the mixing angles

It is pointed out that Fritzsch's derivation of the mixing angles for a six-quark theory based on a SU(2)_L × SU(2)_R × U(1) model is in error. The correct formula for the mixing angles differs significantly from Fritzsch's results.