Vacuum expectation values from fusion of vertex operators

The algebra of fused vertex operators for the ABF model is defined and studied in the free fields approach. Vacuum expectation values of local operators in the scaling theory are reproduced from the matrix elements of the fused vertex operators.     

Discrete symmetry groups of vertex models in statistical mechanics

We analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations. They can be seen as generated by involutions corresponding respectively to two kinds of transformations onq×q matrices: the inversion of theq×q matrix and an (involutive) permutation of the entries of the matrix. We show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics. This approach enables one to analyze two-dimensionalq ⁴-state vertex models as simply as three-dimensional vertex models, or higher-dimensional vertex models. Various examples of birational symmetries of vertex models are analyzed. A particular emphasis is devoted to a three-dimensional vertex model, the 64-state cubic vertex model, which exhibits a polynomial growth of the complexity of the calculations. A subcase of this general model is seen to yield integrable recursion relations. We also concentrate on a specific two-dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes Yang-Baxter integrable. It is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces, or higher-dimensional algebraic varieties.     

Regge vertex for quark production in the central rapidity region in the next-to-leading order

The effective vertex for quark production in the interaction of a Reggeized quark and a Reggeized gluon is calculated in the next-to-leading order (NLO). The resulting vertex is the missing component of the NLO multi-Regge amplitude featuring quark and gluon exchanges in the t channels. This calculation will make it possible to develop in future the bootstrap approach to proving quark Reggeization in the next-to-leading logarithmic approximation.     

On inclusive gluon jet production off the nucleus in perturbative QCD

In the perturbative QCD approach single and double inclusive cross-sections for gluon production off the nucleus are studied by the relevant reggeized gluon diagrams. Various terms corresponding to emission of gluons from the triple pomeron vertex are found. Among them the term derived by Kovchegov and Tuchin emerges as a result of the transition from the diffractive to effective high-energy vertex. However it does not exhaust all the vertex contributions to the inclusive cross-section. In the double inclusive cross-section a contribution violating the naive AGK rules is found in which one gluon is emitted from the vertex and the other from one of the two pomerons below the vertex. But then this contribution is subdominant at high energies and taking it into account seems to be questionable.Received: 6 March 2005, Revised: 5 May 2005, Published online: 8 June 2005     

An efficient approach for feature-preserving mesh denoising

With the growing availability of various optical and laser scanners, it is easy to capture different kinds of mesh models which are inevitably corrupted with noise. Although many mesh denoising methods proposed in recent years can produce encouraging results, most of them still suffer from their computational efficiencies. In this paper, we propose a highly efficient approach for mesh denoising while preserving geometric features. Specifically, our method consists of three steps: initial vertex filtering, normal estimation, and vertex update. At the initial vertex filtering step, we introduce a fast iterative vertex filter to substantially reduce noise interference. With the initially filtered mesh from the above step, we then estimate face and vertex normals: an unstandardized bilateral filter to efficiently smooth face normals, and an efficient scheme to estimate vertex normals with the filtered face normals. Finally, at the vertex update step, by utilizing both the filtered face normals and estimated vertex normals obtained from the previous step, we propose a novel iterative vertex update algorithm to efficiently update vertex positions. The qualitative and quantitative comparisons show that our method can outperform the selected state of the art methods, in particular, its computational efficiency (up to about 32 times faster).     

Ground state properties of a spin-3/2 model on a decorated square lattice

We present the construction of an optimum ground state for a quantum spin-3/2 antiferromagnet. The spins reside on a decorated square lattice, in which the basis consists of a plaquette of four sites. By using the vertex state model approach we generate the ground state from the same vertices as those used for the corresponding ground state on the hexagonal lattice. The properties of these two ground states are very similar. Particularly there is also a parameter-controlled phase transition from a disordered to a Néel ordered phase. In the regime of this transition, ground state properties can be obtained from an integrable classical vertex model. Received 28 June 1999     

Peratization of the vertex in the theory of weak interactions with the W-meson

The integral equation for the vertex with crossed boson lines is solved by the known peratization technique. In the zero energy approach some numerical corrections to the simple vertex are obtained and it is shown that higher order corrections cannot be neglected. The influence of these corrections on the cross-section for the neutrino production of the W-meson in the nuclear field and on the W-mass is investigated.This work is a part of a thesis written in 1965 at the Faculty of Technical and Nuclear Physics of The Czech Technical University in Prague.     

Full fermion-boson vertex function derived in terms of symmetry relations in Abelian gauge theory

Nonperturbative studies such as confinement and dynamical chiral symmetry breaking need the nonperturbative interacting vertex functions. In this paper, an approach to determining the full fermion-boson vertex function in four-dimensional Abelian gauge theory is presented: this full vertex function is derived in terms of a set of normal (longitudinal) and transverse Ward-Takahashi relations for the fermion-boson (vector) and axial-vector vertices in the momentum space in the case of massless fermion. Such a derived fermion-boson vertex function should be satisfied both perturbatively and nonperturbatively. The fact that such a derived full fermion-boson vertex function to one-loop order holds indeed is proven and the nonperturbative form of this vertex is also under discussion.     

On the phenomenological three-graviton vertex

In General Relativity, the graviton interacts in three-graviton vertex with a tensor that is not the energy-momentum tensor of the gravitational field. We consider the possibility that the graviton interacts with the definite gravitational energy-momentum tensor that we previously found in the G ² approximation. This tensor in a gauge, where nonphysical degrees of freedom do not contribute, is remarkable, because it gives positive gravitational energy density for the Newtonian center in the same manner as the electromagnetic energy-momentum tensor does for the Coulomb center. We show that the assumed three-graviton vertex does not lead to contradiction with the precession of Mercury’s perihelion. In the S-matrix approach used here, the external gravitational field has only a subsidiary role, similar to the external field in quantum electrodynamics. This approach with the assumed vertex leads to the gravitational field that cannot be obtained from a consistent gravity equation.     

A Second-row Parking Paradox

We consider two variations of the discrete car parking problem where at every vertex of ℤ cars (particles) independently arrive with rate one. The cars can park in two lines according to the following parking (adsorption) rules. In both models a car which arrives at a given vertex tries to park in the first line first. It parks (sticks) whenever the vertex and all of its nearest neighbors are not occupied yet. A car that cannot park in the first line will attempt to park in the second line. If it is obstructed in the second line as well, the attempt is discarded. In the screening model a) a car cannot pass through parked cars in the second line with midpoints adjacent to its vertex of arrival. In the model without screening b) cars park according to the same rules, but parking in the first line cannot be obstructed by parked cars in the second line. We show that both models are solvable in terms of finite-dimensional ODEs. We compare numerically the limits of first- and second-line densities, with time going to infinity. While it is not surprising that model a) exhibits an increase of the density in the second line from the first line, more remarkably this is also true for model b), albeit in a less pronounced way.     

Symmetric vertex models on planar random graphs

We solve a 4-(bond)-vertex model on an ensemble of 3-regular (Φ³) planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The method of solution, by mapping onto an Ising model in field, is inspired by the solution by Wu et.al. of the regular lattice equivalent – a symmetric 8-vertex model on the honeycomb lattice, and also applies to higher valency bond vertex models on random graphs when the vertex weights depend only on bond numbers and not cyclic ordering (the so-called symmetric vertex models).The relations between the vertex weights and Ising model parameters in the 4-vertex model on Φ³ graphs turn out to be identical to those of the honeycomb lattice model, as is the form of the equation of the Ising critical locus for the vertex weights. A symmetry of the partition function under transformations of the vertex weights, which is fundamental to the solution in both cases, can be understood in the random graph case as a change of integration variable in the matrix integral used to define the model.Finally, we note that vertex models, such as that discussed in this paper, may have a role to play in the discretisation of Lorentzian metric quantum gravity in two dimensions.     

The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge

The Dyson-Schwinger equation for the ghost-gluon vertex of the Hamiltonian approach to Yang-Mills theory in Coulomb gauge is solved at one-loop level using as input the non-perturbative ghost and gluon propagators previously determined within the variational approach. The obtained ghost-gluon vertex is IR finite but IR enhanced compared to the bare one by 15%-25%, depending on the kinematical momentum regime.     

Regge behaviour at high energy and more on boson-fermion interaction

Our approach to the problem of boson-fermion interaction in the conventional RFT stems from a model of super-symmetric version in 2-space and 1 time world. Basically it is stressed here that at super high energy there may not be any distinction between the bosonic and fermionic modes and may be treated on a common footing. Usual renormalization group approach for the vertex function has been adopted and the characteristic functionsβ ₁ andβ ₂ are calculated and the possibility of having stable points in the theory has been studied.     

Calculation of Tensor Susceptibility Beyond Rainbow-Ladder Approximation

In this paper, we extend the calculation of tensor vacuum susceptibility in the rainbow-ladder approximation of the Dyson–Schwinger (DS) approach in Shi et al. (Phys Lett B 639:248, 2006) to that of employing the Ball–Chiu (BC) vertex. The dressing effect of the quark-gluon vertex on the tensor vacuum susceptibility is investigated. Our results show that compared with its rainbow-ladder approximation value, the tensor vacuum susceptibility obtained in the BC vertex approximation is reduced by about 10%. This shows that the dressing effect of the quark-gluon vertex is not large in the calculation of the tensor vacuum susceptibility in the DS approach.     

Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion. It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.     

Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion.It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.     

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in nongrowth random networks.In this model,we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it.The network evolves according to a vertex strength preferential selection mechanism.During the evolution process,the network always holds its total number of vertices and its total number of single-edges constantly.We show analytically and numerically that a network will form steady scale-free distributions with our model.The results show that a weighted non-growth random network can evolve into scale-free state.It is interesting that the network also obtains the character of an exponential edge weight distribution.Namely,coexistence of scale-free distribution and exponential distribution emerges.     

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.     

Localization for a Nonlinear Sigma Model in a Strip Related to Vertex Reinforced Jump Processes

We study a lattice sigma model which is expected to reflect Anderson localization and delocalization transition for real symmetric band matrices in 3D, but describes the mixing measure for a vertex reinforced jump process too. For this model we prove exponential localization at any temperature in a strip, and more generally in any quasi-one dimensional graph, with pinning (mass) at only one site. The proof uses a Mermin–Wagner type argument and a transfer operator approach.     

Three-Dimensional Vertex Model Related BCC Model in Statistical Mechanics

In this paper, a three-dimensional vertex model is obtained. It is a duality of the three-dimensional integrable lattice model with N states proposed by Boos, Mangazeev, Sergeev and Stroganov. The Boltzmann weight of the model is dependent on four spin variables, which are the linear combinations of the spins on the corner sites of the cube, and obeys the modified vertex-type tetrahedron equation. This vertex model can be regarded as a deformation of the one related to the three-dimensional Baxter-Bazhanov model. The constrained conditions of the spectrums are discussed in detail and the symmetry properties of weight functions of the vertex model are presented.