Том 200, № 2 (2019)

In the framework of the quark–gluon string fusion model on the transverse lattice, we study a strongly intensive variable characterizing correlations between the number of particles produced in hadronic interactions in two observation windows separated by a rapidity interval. We show that in the case of independent identical strings, this variable is indeed strongly intensive. It depends only on string characteristics and is independent of trivial so-called volume fluctuations in the string number resulting, in particular, from inevitable impact parameter fluctuations. With string fusion effects causing the production of string clusters with new properties taken into account, this variable turns out to be equal to the weighted average of its values for different string clusters. The weighting coefficients depend on the collision conditions, and the variable loses its strongly intensive character. In the framework of this model in a realistic case with a nonuniform string distribution in the transverse plane, we find explicit analytic formulas for the asymptotic coefficients of long-range correlations between different quantities including an intensive one, the average transverse momentum. We analyze the properties of the obtained correlation coefficients, the studied strongly intensive variable, and also the possibilities of its experimental observation.

We show that effects similar to those for a rotating black hole arise for an observer using a uniformly rotating reference frame in a flat space-time: a surface appears such that no body can be stationary beyond this surface, while the particle energy can be either zero or negative. Beyond this surface, which is similar to the static limit for a rotating black hole, an effect similar to the Penrose effect is possible. We consider the example where one of the fragments of a particle that has decayed into two particles beyond the static limit flies into the rotating reference frame inside the static limit and has an energy greater than the original particle energy. We obtain constraints on the relative velocity of the decay products during the Penrose process in the rotating reference frame. We consider the problem of defining energy in a noninertial reference frame. For a uniformly rotating reference frame, we consider the states of particles with minimum energy and show the relation of this quantity to the radiation frequency shift of the rotating body due to the transverse Doppler effect.

Using the field theory renormalization group technique in the framework of the so-called double-expansion scheme, which takes additional divergences that appear in two dimensions into account, we calculate the turbulent Prandtl number in two spatial dimensions in the two-loop approximation in the model of a passive scalar field advected by the turbulent environment driven by the stochastic Navier–Stokes equation. We show that in contrast to the three-dimensional case, where the two-loop correction to the one-loop value of the turbulent Prandtl number is very small (less than 2% of the one-loop value), the two-loop value of the turbulent Prandtl number in two spatial dimensions, Pr_t = 0.27472, is considerably smaller than the corresponding value Pr_t⁽¹⁾ = 0.64039 obtained in the one-loop approximation, i.e., the two-loop correction to the turbulent Prandtl number in the two-dimensional case represents about 57% of its one-loop value and must be seriously taken into account. This result also means that there is a significant difference (at least quantitatively) between diffusion processes in two- and three-dimensional turbulent environments.

The tensor hierarchy of exceptional field theories contains gauge fields satisfying certain Bianchi identities with sources determining the interactions with standard and exotic branes. These identities are responsible for tadpole cancellation in compactification schemes and provide consistency constraints for building cosmological models. In detail, we consider and develop an approach in which the analysis of the reduction of a (10+10)-dimensional double field theory to a (D+d+d)-dimensional split double field theory allows considering all Bianchi identities of the theory in a form analogous to the extended field theory approach.

Leading logarithms in massless nonrenormalizable effective field theories can be computed using nonlinear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity, analyticity, and crossing symmetry of scattering amplitudes and generalize the renormalization group technique to the case of nonrenormalizable effective field theories. We review the existing exact solutions of nonlinear recurrence relations relevant for field theory applications. We introduce a new class of quantum field theories (quasirenormalizable field theories) in which resumming leading logarithms for 2→2 scattering amplitudes yields a possibly infinite number of Landau poles.

We propose a method for using functional equations to calculate Feynman integrals analytically. We describe the algorithm for solving the functional equations and show that a solution of a functional equation for the Feynman integral is a combination of several integrals with fewer kinematic variables. In some cases, using the functional equations, we can also reduce these integrals to integrals with even fewer variables. Such a stepwise application of the functional equations leads to integrals that can be calculated more simply than the original integral. We apply the proposed method to several one-loop integrals. For the three-point and four-point integrals with massless propagators and an arbitrary space dimension d, we obtain analytic expressions in terms of hypergeometric functions.

In papers devoted to superfluidity, the generally accepted statement that the dynamics of the corresponding phase transition is described by the stochastic model F or E can be frequently found. Nevertheless, the dynamical critical index has not been found even in the leading order of the perturbation theory. It is also unknown which model, E or F, in fact corresponds to this system. We use two different approaches to study this problem. First, we study the dynamics of the critical behavior in a neighborhood of the λ point using the renormalization group method based on a quantum microscopic model in the formalism of the time-dependent Green’s functions at a finite temperature. Second, we study the stochastic model F to find whether it is stable under compressibility effects. Both approaches lead to the same very unexpected result: the dynamics of the phase transition to the superfluid state are described by the stochastic model A with a known dynamical critical index.