Analytic study of θ vacua on the lattice

A new definition of the topological charge density for four-dimensional lattice gauge theory is given. Using a systematic expansion we find a cusp in the vacuum energy at θ = π signaling the spontaneous breaking of CP there. Unlike its two-dimensional analogue (QED₂), QCD confines at θ = π. As a by-product an expression for the topological mass term for (2+1)-dimensional lattice gauge theory is obtained.     

Kauffman knot polynomials in classical abelian Chern-Simons field theory

Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant t^I(L) is constructed for a link L, where I is the abelian Chern-Simons action and t a formal constant. For oriented knotted vortex lines, t^I satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, t^I satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.     

Antiferroelectric spin wave resonance

Antiferroelectric spin wave resonance (AFESWR) and electric spin moment, mathematically predicted by Dirac, were identified for the first time. It has also been found, in addition to well-known SSH-model, that topological quasiparticles, called σ-quasiparticles, can be formed in CC σ-bonds of organic polymers. Topological σ-polaron lattice is proposed to be responsible for the observed AFESWR both in starting polyvinylidene fluoride (PVDF) films and in carbynoid films, which are the products of PVDF-dehydrohalogenation. Dynamical systems of σ-polarons and π-solitons, identified in the samples studied, are substantionally nonlinear and can be registered in stochastic regime by usual IR absorption measurements.     

作用表示波动方程中与面有关项

这篇短文的内容是:(i)对於量子场论中的i(δψ[σ])/(δσ(x))=V(x,σ)ψ[σ] 如何由寻常的“曲面上的薛定谔方程”导出,作一个较严格的讨论,以及 (ii)讨论上式中的V(x,σ)在什么条件下不包含有σ。我们证明了所需的条件是 (?L^I)/(?φ_μ) (?L^I)/(?φ_ν)=(?²L)/(?φ_μ?φ_ν)F(φ,φ_ρ),式中L,L^I代表总拉格朗日及作用拉格朗日,φ代表场量,φ_μ代表φ/x^μ,F(φ,φ_ρ)代表φ及φ_μ的一个任意函数。     

Calculation of the pion-nucleon σ term value from the experimental data on pionic atoms

The pion-nucleonσ term value is calculated using pion-nuclear scattering lengths extracted from the data on pionic atoms withA≦24 and isospinI = 0. The renormalization of the soft-pionπN amplitude in nuclear matter is taken into account. TheA-dependence of the pion-nuclear scattering lengths is studied. Comparison with other results forσ term leads to the conclusion that the most probable interval for it is 30–50 MeV. The dispersive part of theS-wave pion-nuclear potential is discussed.     

Measurement of L X-ray fluorescence cross sections and relative intensities for some elements in the atomic range 78 ≤ Z ≤ 92

The L X-ray fluorescence cross sections (σ_Ll, σ_Lα, σ_Lη, σ_Lβ, σ_Lβ6, σ_Lβ2,₄, σ_Lβ1,₃, σ_Lβ9,10, σ_Lγ, σ_Lγ1, σ_Lγ2,3, σ_Lγ4 and σ_Lγ5) and relative intensities (I_Lα, I_Ll, I_Lη, I_Lβ, I_Lβ6, I_Lβ2,4, I_Lβ1,3, I_Lβ9,10, I_Lγ, I_Lγ1, I_Lγ2,3, I_Lγ4 and I_Lγ5) for some elements in the atomic range 78 ≤ Z ≤ 92 have been measured at 59.54 keV photons energies from an Am-241 point source. The L X-rays emitted by samples have been counted by a Si(Li) detector. The L X-ray fluorescence cross sections and relative intensities have been also calculated theoretically by using atomic parameters. The measured values have been compared with the theoretical values.     

θ renormalization, electron-electron interactions and super universality in the quantum Hall regime

The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of θ renormalization by instantons. Within the generalized non-linear σ model approach initiated by Finkelstein we obtain the physical observables of the interacting electron gas, formulate the general (topological) principles by which the Hall conductance is robustly quantized and derive—for the first time—explicit expressions for the non-perturbative (instanton) contributions to the renormalization group β and γ functions. Our results are in complete agreement with the recently proposed idea of super universality which says that the fundamental aspects of the quantum Hall effect are all generic features the instanton vacuum concept in asymptotically free field theory.     

Triangulated random surfaces

A model of discretized random surfaces that contains the extrinsic curvature as well as the usual area term in the action is considered. The renormalization group predicts that at large distances the model is indistinguishable from previous proposals of triangulated surfaces that contained only the area term, but, unlike them, does not grow spikes. The partition function and all its moments are finite and well defined. The model is solved for large d in the vicinity of the IR fixed point. The Hausdorff dimension is ∞ and the entropy exponent agrees with the one obtained by Zamolodchikov and others for the Polyakov action in the continuum.     

Renormalization of two-dimensional R2-gravity

Two-dimensional gravity with an R²-term is quantized around the R2-Liouville solution in the semiclassical way. Renormalization, regularization (infra-red, ultra-violet) and a topological term ∂ (ϕ∂ϕ)) ) are carefully treated. All (1-loop) divergences are renormalized by the cosmological constant (μ) and the R2-coupling-constant (β) for the case β > 0. The quantum meaning of the topological term is clarified. The renormalization group beta-functions of the couplings β and μ are obtained. It is found that the theory is conformal (i.e. the if beta-functions = 0) for w = (β/A) · (16π · 48π/(26 − c_m)) ⩾ 1 (where A is a fixed area) exactly when the coupling constant ξ of the topological term takes the value of 1. As for 0 < w < 1, β is asymptotically free for c_m < 26 and μ is asymptotically non-free.     

Theory of the quantized Hall effect (I)

This is the first of a series of three papers presenting a field theoretic approach to the (integrally) quantized Hall effect. The basic idea is that the transverse conductivity σ_xy directly couples to a topological quantum number characterizing the phase relationship between advanced and retarted electron propagators. This allows us to present a reformulation of the Laughlin quantization argument as well as a direct demonstration of the breakdown of the two-dimensional scaling theory of localization. This paper summarizes all our results and discusses a physical picture of the emergence of extended states.     

UV absorption of RbAg4I5-RE (Sm, Yb) thin-film systems

UV spectra of samples prepared by vacuum deposition of Sm and Yb thin films on 100–200-nm thick films of the RbAg₄I₅ solid electrolyte (SE) at 300–350 K contain strong absorption bands peaking at about 4.3 and 5.0 eV. After deposition of ～5 nm of Sm, the ionic conductivity σ of the samples decreases from σ ₀ to ≈0.9 σ ₀, and the SE lattice parameter, from 11.24 to ≈11.15 Å, with the x-ray reflection halfwidth increasing from 0.5 to 0.8°. Further growth of Sm concentration in the samples changes the x-ray diffraction pattern, the absorption at 4.3 and 5.0 eV increases, a new absorption edge forms at 3.8 eV, and σ decreases down to ～10^?2 σ ₀. It is conjectured that the strong UV absorption bands in heavily defected silver halides of the RbAg₄I₅-Sm(Yb) system is genetically related to the 4d ¹⁰→4d ⁹5s electronic transitions in free Ag⁺ ions.     

Quantum gauge fields and flat connections in 2-dimensional BF theory

The 2-dimensional BF theory is both a gauge theory and a topological Poisson σ-model corresponding to a linear Poisson bracket. In [3], Torossian discovered a connection which governs correlation functions of the BF theory with sources for the B-field. This connection is flat, and it is a close relative of the KZ connection in the WZW model. In this Letter, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.     

A path-functional field theory of lattice gauge models and the large-N limit

We transform lattice gauge models to a theory of functional fields defined on a set of closed paths. Some relevant properties of the formalism are discussed in detail, with emphasis on symmetry and topological structure. We then investigate the large-N limit of the U(N) lattice gauge model in arbitrary dimensions using this formalism. Assuming the existence of the limit, we show, to arbitrary order of the strong coupling expansion parameter (g²N)^?, which is kept fixed, that for the leading contribution in the limit: (i) the flow of indices in color space can be represented by planar diagrams; (ii) when the diagrams are immersed in space-time they are random surfaces without handles; (iii) there are interactions of the surfaces which can be depicted as the formation of multisheet bubblesw in the surfaces. This formalism also makes it possible to set up a gauge-invariant mean-field approximation.     

LEED studies of vicinal surfaces of germanium

Clean germanium surfaces inclined at small angles to (111), (100) and (110) planes were investigated by LEED. Surfaces with orientations close to (111) and (100) are stepped and regular steps are retained in the whole temperature range investigated.Steps with (111) terraces and edges towards $\text{[2}\text{1}\text{1}\text{]}$ have a height of about one interplanar distance d₁₁₁ at all temperatures, and steps with edges towards $\text{[}\text{2}\text{11]}$ have a height of about two interplanar distances below 500°C and of about one interplanar distance above 500°C. Steps with (100) terraces and edges in the [011] direction have a height about two interplanar distances d₁₀₀. The surfaces with orientations close to (110) are facetted at room temperature. The (17 15 1) facets are present on the surfaces oriented in the $\text{[}\text{1}\text{10]}$ zone and the (10 9 2) facets on the surfaces oriented in the [001] zone. At high temperatures (about 480 and 770°C respectively) a reversible structural reconstruction of these surfaces into stepped ones takes place.     

Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”

The distribution functions and the free energy are expressed in terms of the effective fields for the regular and random Ising models of an arbitrary spin S on the generalized cactus tree. The same expressions apply to systems on the usual lattice in the “cactus approximation” in the cluster variation method. For an ensemble of random Ising models of an arbitrary spin S on the generalized cactus tree, the equation for the probability distribution function of the effective fields is set up and the averaged free energy is expressed in terms of the probability distribution. The same expressions apply to the system on the usual lattice in the “cactus approximation”. We discuss the quantities on the usual lattice when the system or the ensemble of random systems has the translational symmetry. Variational properties of the free energy for a system and of the averaged free energy for an ensemble of random systems are noted. The “cactus approximations” are applicable to the Heisenberg model as well as to the Ising model of an arbitrary spin, and to ensembles of random systems of these models.     

Quantum group invariant integrable n-state models with periodic boundary conditions

Using the methods of topological quantum field theory we construct aU _q [sl(n)] invariant integrable transfer matrix for the case ofq being a root of unity. It corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. its interior. By means of the nested Bethe ansatz method we analyse conformai properties and discuss the representational content of the Bethe ansatz solutions.     

Debye-waller factor for electron scattering by surface atoms

The contribution of anharmonic atomic vibrations to the EXAFS-spectrum is described by the third cumulantσ(³) which contributes with a term proportional tok ³ to the phase in the single scattering plane wave approximation. Due to the lattice expansion and enhancedσ(²) in the surface region we get additional temperature dependent contributions, which are evaluated in a curved wave theory. Transforming this expression into the basic formula we get an additional term proportional tok ³ in the phase of the generalized scattering amplitude. This valueΔα(³) has to be subtracted to get a value forσ(³). Numerical results at the O-K-edge of NiO give a value forΔσ(³) of about 10^?4 ų.     

A four-dimensional non-linear σ-model

We study a four-dimensional version of the non-linear O(n) σ-model in Euclidean space, introducing a suitable kinetic term in order to have a theory with many of the properties of the two-dimensional model. The outcoming theory is shown to be ultraviolet free for n > 2. Its behaviour is then discussed in the large-n expansion. It is found that in general two phases exist, in one symmetry is broken, in the other preserved, and both are possible in four dimensions. For a range of values of the coupling constant both asymptotic freedom and the perturbative expansion are valid, contrary to the situation of the two-dimensional σ-model. The infrared behaviour is found to be regular and a singularity of the running coupling constant to be of no relevance for the Green functions.     

Pion pair production in γ-γ collisions at low energy and the born cross section

It is shown that (i) there is a severe constraint on σ(γγ→π⁺π⁻/σ_Born imposed by phenomenological theory and (ii) the low-mass π⁺π⁻ enhancement observed in the reaction γγ→π⁺π⁻ comes from interference between the Born term and the correction term.