SU(2) gluodynamics above the deconfinement temperature

A physical model for describing SU(2) gluodynamics above the deconfinement temperature is developed on the basis of the operator-product-expansion method. The properties of the nonperturbative vacuum are parametrized in terms of gauge-invariant gluomagnetic correlation functions. The free energy of the system is calculated for T>T _c. The results obtained within the proposed model for the thermal properties of gluons (energy density, nonideality) are shown to agree with data coming from lattice calculations.     

Sphaleron Transition Rate in Lattice Gluodynamics

The sphaleron transition rate in gluodynamics at the temperature T /T_c = 1.24 has been calculated by lattice simulation. The calculations involve the Kubo formula, which relates the sphaleron transition rate to the correlation function of the topological charge density. The gradient flow method has been used to calculate the correlation function of the topological charge density. The Kubo formula has been inverted by the Backus–Gilbert method. The results have been compared to those obtained by other methods.     

Behavior of the beta function in SU(2) thermodynamics on a lattice

The beta function on a lattice is studied in SU(2) gluodynamics. The definition of the beta function within the scaling hypothesis at a finite lattice size is used. The functions obtained in this way are compared with the results known in the continuum limit. Graphics processing units are used as a computing platform, whereby a large amount of statistical data have been accumulated. Beta functions are analyzed for a large number of various lattices. It is shown that the beta function being studied complies with the respective analytic expression in the phase-transition region. A fast method that makes it possible to estimate the critical value of the coupling constant on a lattice is proposed.     

Dilaton effective lagrangian in gluodynamics

The lagrangian of gluodynamics does not contain dimensional parameters. As a consequence, there emerges an infinite set of Ward identities connecting n-point functions induced by the operator σ = θ_μμ, where θ_μv stands for the regularized energy-momentum tensor. We construct an effective (tree) lagrangian which includes one scalar meson field and saturates automatically all the Ward identities.     

Thermal monopoles in the SU(2) gauge theory on a lattice

Color-magnetic thermal monopoles in SU(2) lattice gluodynamics with improved Simanzik action were studied. The density of the monopoles, the monopole chemical potential, the cluster susceptibility, and the cluster magnetization were studied. These results were compared with results that were reported elsewhere.     

Correlation length of the vacuum condensate in lattice gauge theories

The correlation length λ of the vacuum condensateG ₂ is determined by Montecarlo simulation of anSU(2) lattice gauge theory. The result isG ₂ λ⁴ = 0.0019 ± 0.0002. The implications of this result are discussed.     

Neutral ρ meson in a strong magnetic field in the SU(2) lattice gauge theory

The correlation functions of vector and pseudoscalar currents have been calculated in the external strong magnetic field in SU(2) lattice gluodynamics. The masses of the neutral ρ meson with different spin projections s = 0, ±1 to the axis parallel to the external magnetic field B have been calculated. The ρ meson mass with zero spin s = 0 decreases with the growth of the magnetic field and the ρ meson masses with s = ±1 increase with the magnetic field.     

An additional symmetry in the Weinberg-Salam model

An additional Z₆ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper, we report our results on the numerical simulation of its electroweak sector.     

Monopole order parameter in SU(2) lattice gauge theory

We report the results of numerical calculations for the probability distribution of the values of the monopole creation operator Ф_mon in the maximal Abelian projection of SU(2) lattice gluodynamics. It turns out that at low temperature in the confinement phase the maximum of the distribution corresponds to a nonzero value of the field Ф_mon. This means that the effective potential has the form of a Higgs potential. Above the phase-transition point the minimum of the potential (the maximum of the distribution of the monopole creation operator) corresponds to a zero value of the monopole field Fmon. The results presented are a direct proof of the existence of a condensate of Abelian monopoles in the confinement phase of gluodynamics, and they confirm the hypothesis that the vacuum of gluodynamics is analogous to a dual superconductor. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 392–397 (25 March 1996)     

Monopoles in gluodynamics and blocking from continuum to lattice

We review the method of blocking of topological defects from continuum to lattice as a nonperturbative tool to construct effective actions for these defects. The actions are formulated in the continuum limit, while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. We demonstrate the success of the method in deriving the effective actions for Abelian monopoles in the pure SU(2) gauge models in an Abelian gauge. In particular, we discuss the gluodynamics in three and four spacetime dimensions at zero and nonzero temperatures. Besides the action, the quantities of our interest are the monopole density, the magnetic Debye mass, and the monopole condensate.     

Shear viscosity of superfluid He-A1 at low temperatures

The shear viscosity tensor of the A₁-phase of superfluid ³He is calculated at low temperatures and melting pressure, by using the Boltzmann equation approach. The two normal and superfluid components take part in elements of the shear viscosity tensor differently. The interaction between normal and Bogoliubov quasiparticles in the collision integrals is considered in the binary, decay, and coalescence processes. We show that the elements of the shear viscosities η_xy, η_xz, and η_zz are proportional to (T/T_c)⁻². The constant of proportionality is in nearly good agreement with the experimental results of Roobol et al.     

Surface diffusion and formation of ordered state

Surface diffusion and formation for an ordered phase is investigated using the lattice gas model in Monte-Carlo simulation. Interaction up to the second nearest neighbour between particles is considered. The coverage is calculated as a function of a normalized coordinate by the square root of the diffusion time, starting from the initial step coverage. When the temperature T is lower than T_c, a shoulder appears in the coverage curve at near half coverage. It is shown that this shoulder corresponds to the formation of a c(2 × 2) phase, in which the existence of long range order is confirmed. On the other hand, when T is higher than T_c, the shoulder in the coverage curve disappears, but the short range order of the first and second nearest neighbour correlation still remains and the formation of islands of c(2 × 2) pattern is locally observed. The microscopic growth mechanism of the c(2 × 2) phase is considered. The observed growth rate is explained phenomenologically through the diffusion coefficient which is concentration-dependent.     

Two-loop corrections to the correlation function for tensor currents in gluodynamics

The results of evaluating the leading-order a_s corrections to the correlation function for tensor currents in pure gluodynamics are presented. These corrections to the parton result for the correlation function are not large numerically, which allows one to use perturbation theory to analyze the resonance spectrum within the sum-rule method.     

Lower dimension vacuum defects in lattice Yang-Mills theory

We overview lattice data on d = 0, 1, 2, 3 dimensional vacuum defects in lattice four-dimensional SU(2) (SU(3)) gluodynamics. In all the cases, defects have a total volume which scales in physical units (with zero fractal dimension). In the case of d = 1, 2, the defects are distinguished by ultraviolet divergent non-Abelian action as well. This sensitivity to the ultraviolet scale allows us to derive strong constraints from the continuum theory on the properties of the defects, which turn out to be satisfied by the lattice data. We discuss a classification scheme of the defects which allows us to (at least) visualize the defect properties in a simple and unified way. A not-yet-checked relation of the defects to the spontaneous chiral symmetry breaking is suggested by the scheme. Finally, we present some arguments that the defects considered could become fundamental variables of a dual formulation of the theory.     

A background-dependent approach to the theory of gravitation II. Relativistic gravitational equations

On the basis of the results of Paper I and guided by a Machian view of nature, we find new gravitational equations which are background dependent. Such equations describe a purely geometrical theory of gravitation, and their dependence on the background structure is through the total energy-momentum tensor on the past sheet of the light cone of each space-time pointx [θ^μν x, say], i.e., through the integral on the past sheet of the light cone ofx of the parallel transport of the energy-momentum tensor from the space-time point in which it is defined tox along the geodesic connecting the two space-time points. Following Gürsey, we assume that the source of the De Sitter metric is not the cosmological term, but, rather, the energy-momentum tensor of a “uniform distribution of mass scintillations” [T ^μν x, say].T ^μν x, indeed, turns out to be equal to the metric tensor times a constant factor. As a consequence, in any local inhomogeneity A of a space-time whose background structure is determined by the Perfect Cosmological Principle,θ ^μν turns out to be approximately equal to the metric tensor times a constant factor, providedT=g _αβ T ^αβ is sufficiently small and the structure of the past sheet of the light cones of the space-time points belonging to Λ is not too much perturbed by the local gravitational field. As a consequence, in Λ the new equations approximately reduce to Einstein's equations. If one considers a “superuniverse model” in which our universe is considered as a local inhomogeneity in a De Sitter background, then from the above result there follows a fortiori the agreement of the new gravitational equations with the classical tests of gravitation. Furthermore, the dependence on the background structure is such that the new equations (i) incorporate the idea that the frame has to be fixeddirectly in connection with cosmological observations, and (ii) are singular in the absence of matter in the whole space-time. Moreover, (iii) the coupling constant turns out to be dimensionless in natural units (c=1=?), and (iv) a local inertial frame in a De Sitter background is determined by the condition that with respect to it the background structure is homogeneous in space and in time and is Lorentz invariant.     

Alternative scaling hypothesis forSU(2) andSU(3) lattice gauge theories

High precision data from a variety of sources forSU(2) andSU(3) Wilson action lattice gauge theory are analyzed with respect to the hypothesis of the possible existence of a zero temperature deconfining phase transition, in analogy with theU(1) theory. The internal energy, specific heat, string tension, and Wilson line, fit well to correlation length scaling laws associated with a finite order transition occurring at the weak coupling end of the crossover region for both theories. TheSU(2) theory is consistent with a correlation length exponent ν=2/3 and critical pointβ _c ≈2.47. ForSU(3) the data fit well to ν=1 andβ _c ≈6.69. Additional indirect evidence for the existence of such phase transitions is discussed, as is the possible crucial role of light dynamical fermions in the confinement mechanism.     

Theoretical study of the susceptibility of nearly one-dimensional VF2

The paramagnetic susceptibility of a nearly one-dimensional helical magnet VF₂, of the tetragonal body-centered lattice, is calculated on the assumption of classical spins which form linear chains along the c-axis, with strong intra-chain and weak inter-chain exchange coupling. The partition function and the susceptibility are expanded in powers of J′/k_BT, J′ being the inter-chain coupling constant. The coefficients of the expansion are expressible in terms of spin correlation functions for independent linear chains. The susceptibility up to the 3rd power of independent linear chains. The susceptibility up to the 3rd power of J′/k_BT shows, as a function of temperature, a pronounced broad maximum as observed. The specific heat calculated with classical spins fails to reproduce the observation.     

Finite size scaling of spin-spin correlations on the Ising square lattice

Using Monte Carlo data for the Ising square lattice, we show that the row spin-spin correlation functions scale as a function of both lattice size and ? = ∣1 ? T/T_c∣ forT >T_c.     

Unitary group decomposition of hamiltonian operators. II. SU (4) irreducible tensors,norms and their energy variation and symmetry breaking

SU(6) ? SU(4) tensor decomposition of effective interactions in the 2s-1d shell has been carried out to examine the relative importance of the various irreducible tensors in many-particle spaces. For this purpose norms of the irreducible tensors are evaluated in many-particle spaces. Variation of the expectation value of the square of the irreducible tensor parts with excitation energy has also been examined using the polynomial expansion method. A new measure of symmetry breaking that is theoretically more sound is derived which includes in its definition partial width as well as internal width. This is used to study SU(4) symmetry mixing in nuclei.