We review the results of applying the statistical field-theoretic approach to the problem of fully developed turbulence in nonrelativistic three-dimensional magnetohydrodynamics (MHD), which have been obtained over the past forty years. The review covers both general aspects of the physics of MHD turbulence and the necessary mathematical machinery of statistical field theory, including elements of renormalization theory and the renormalization-group (RG) method. The approach is illustrated using a stochastic model of stationary, locally homogeneous, fully developed three-dimensional MHD turbulence in the general case of a medium with broken spatial parity (helical MHD). In this model, RG techniques make it possible to establish the existence of several infrared-stable scaling regimes and to calculate the critical dimensions of various composite operators, the infrared asymptotics of correlation functions, and the amplitude factors in scaling laws, as well as to incorporate the effects of compressibility, anisotropy, etc.

For an important class of helical MHD systems, the field-theoretic approach provides an elegant formulation of the fundamental problem of large-scale turbulent dynamo action — namely, the generation of a large-scale magnetic field ⟨b⟩ = B (where b denotes magnetic fluctuations) at the expense of the energy of turbulent fluctuations — via the decay of the initial unstable vacuum state ⟨b⟩ = 0 as a result of dynamical spontaneous symmetry breaking in the spirit of the Coleman-Weinberg mechanism, followed by stabilization of the theory in the vicinity of the new ground state ⟨b⟩ = B (the dynamo regime). The field-theoretic formulation we developed, together with a generalization of the standard Feynman diagrammatic technique to the dynamo regime, not only makes it possible to treat within a unified framework the existing theoretical approaches to helical magnetohydrodynamics (kinematic MHD, large-scale dynamo theory), but also extends the RG formalism to the dynamo regime, which — unlike closure procedures still common in dynamo theory — is particularly well suited for studying statistically stationary turbulent states. The richness of MHD physics in the dynamo regime is illustrated both in the emergence of new effects (Goldstone-type corrections to Alfvén waves, anisotropic corrections associated with the transport of the large-scale field) and in the theoretically predicted strong dependence of the magnetic energy-spectrum slope on the degree of mirror-symmetry breaking.

Having become observable since the pioneering era of cosmic ray physics fragmentation, the events of relativistic nuclei in nuclear emulsions highlight the potential of this method to study extremely cold ensembles of H and He nuclei, thereby advancing the physics of nuclear clustering and, potentially, expanding nuclear astrophysics. Following the presentation of the progress of this method and orientation to the current problems, this review presents the key results and generalizations of the BECQUEREL experiment at JINR, obtained in the study of unstable nuclear states in the relativistic dissociation of a wide variety of nuclei. The productivity of this method is ensured by record-breaking spatial resolution and full sensitivity to relativistic fragments. According to invariant masses based on the most accurate measurements of emission angles in the extremely narrow fragmentation cone, the contributions of the decays of ⁸Be(0⁺), ⁸Be(2⁺), ⁹Be(1.7), ⁹B, ⁶Be, ¹²С(0⁺₂) or the Hoyle state and ¹²C(3^–) have been identified now. The increase in the contribution of ⁸Be(0⁺) with the multiplicity of accompanying α-particles, followed by ⁹B and ¹²C(0⁺₂), has been established. The structure of these states and the diversity of parent nuclei without the influence of the initial energy assume the coalescence of α-particles and nucleons which appear in dissociation. The initial density and duration of the secondary interaction of the latter may be sufficient up to the lowest-energy fusion reactions. Such a scenario requires low-energy physics concepts to interpret the relativistic fragmentation. The usage of automated microscopy for the analysis of irradiation beams from the JINR NICA accelerator complex becomes a modern basis to apply the nuclear emulsion method which has become fundamental in the physics of the micro-world.

This paper presents the investigation of aerogel Cherenkov radiation detectors and the optical characterization of aerogel samples within the framework of the SPD experiment at the NICA accelerator complex, which is under construction at the Joint Institute for Nuclear Research (Dubna, Russia). The transmittance of aerogel samples was measured at the A. Alikhanyan National Science Laboratory (AANL) (Yerevan Physics Institute). Longitudinal transmittance measurements were performed for two distinct aerogel samples. Data analysis and visualization of results were carried out using the OriginPro 8.5 and ROOT software packages. The obtained results were compared with analogous studies performed at other research centers in order to evaluate the reliability, consistency and accuracy of the measurements.

We construct superconformal mechanics with N = 3 and N = 4 supersymmetries that were inspired by analogy with the supersymmetric Schwarzian mechanics. The Schwarzian, being another system with superconformal symmetry, provides insight into the field content of supersymmetric mechanics, most notably, on the number and properties of the fermionic fields involved. Adding more fermionic fields (four in the N = 3 case and eight in the N = 4 case) made it possible to construct systems possessing maximal superconformal symmetries in N = 3 and N = 4, namely osp(3|2) and D(1, 2; α). In the case of N = 4 supersymmetry, we explicitly construct a new variant of N = 4 superconformal mechanics in which all bosonic subalgebras of the D(1, 2; α) superalgebra have a bosonic realization. In addition, the constructed systems involve the so(3) currents whose parameterization is not fixed, which allows one to consider different underlying geometries.

This short review is devoted to the celebration of two major events in quantum physics. The first one is the birth of the concept of Bose–Einstein condensation (1925) and the second is the experimental proof that it does exist and appears in liquid ⁴He simultaneously with superfluidity below the λ-point (1975).
Both of these events are tightly related to the Bogoliubov theory of superfluidity (1947). The existence of condensate in the system of interacting bosons is the key ansatz of this theory. Therefore, the experiments started at JINR-Dubna in 1975 confirmed this prediction of the Bogoliubov theory that superfluidity of liquid ⁴He (He II) should emerge at the same time as the Bose–Einstein condensation.

Corrected:
13 November 2025 (the captions to Figures 1 and 2 were changed)
26 November 2025 (changes were made in formulas (53) and (55))

We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit ω₁ + ω₂ → 0 (or b → i in 2d CFT) and investigate the two-particle case in detail. Corresponding wave functions are described by complex hypergeometric functions in the Mellin–Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter Q-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special ω₁ − ω₂ → 0 (or b → 1) limit. Additionally, two new degenerations to the complex Calogero–Sutherland type models are described.