A review of the achievements in the theoretical study of (magneto)hydrodynamic turbulence by the methods of quantum field theory is presented. The main focus is given to the problem of justification of the Kolmogorov scaling and its violation, the calculation of critical exponents determining the scaling behavior of the statistical correlations of the studied random fields (velocity, magnetic...
D.I.Kazakov (JINR)
RG Equations in Non-renormalizable Theories
We construct the RG equations for the scattering amplitudes and effective potential
In a a set of non-renormalizable theories. We show that they are a consequence of locality
rather than multiplicative renormalizability. These RG equations sum up the leading log terms
in all orders of PT and allow one to explore the...
We consider correlation functions for Poincare and de Sitter invariant states in the corresponding spaces. We study loop corrections to these correlation functions in various charts of these spaces. We find that the correcations contain certain IR contributions which affect the properties of the correlation functions and in certian cases can lead to the violation of the isometry in the loops.
The current status of experimental tests of quantum electrodynamics with heavy ions is briefly reviewed. Special attention is focused on tests of QED in
supercritical regime. According to the standard QED theory, in slow collisions of two bare nuclei with the total charge number larger than the critical value, Z_1+Z_2 > Z_c =173, the initially neutral vacuum can spontaneously decay into the...
Техника функциональных преобразований Лежандра дает возможность получить для функций Грина квантововолевой системы уравнения в виде бесконечной суммы скелетных диаграмм Фейнмана. Если для вывода этих уравнений используется преобразование Лежандра порядка n>1, линиям этих графиков соответствуют полные пропагаторы, а вершинам порядка k<n+1 - полные к-точечные функции Грина. Учет в скелетных...
Time dependent at finite temperature Green functions were used to describe the dynamics of the phase transition of quantum Bose systems to the superfluid state. The obtained renormalization group results contradict the currently accepted dynamic stochastic model E for this phenomenon. With the help of Temperature Green functions, a new model of the phase transition of Fermi systems to the...
The mystery of the nature of dark matter is one of the most
interesting problems of modern theoretical physics. The lack of
progress in attempts to directly detect dark matter allows us to
assume that all effects related to dark matter are purely
gravitational. The key idea of such an approach is to switch from GR
to some modified theory of gravity with more general equations than
the...
Since their invention over 30 years ago, quantum groups and their representations have been playing an important role in mathematical physics. To each semisimple Lie algebra g and a root of unity q,
one can associate the Lusztig’s “divided powers” quantum group at a root of unity. The category of its finite dimensional representations over complex numbers is non-semisimple and has a...
A convenient integral representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional fishnet field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag...
Compatibility of basic equations of the exact renormalization group and their approximate solutions with the equations of motion of generating functionals of Green functions is discussed.
