Manin matrices and Talalaev's formula

We study special class of matrices with noncommutative entries and demonstrate their various applications in integrable systems theory. They appeared in Yu. Manin's works in 87-92 as linear homomorphisms between polynomial rings; more explicitly they read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}]=[M_{kj}, M_{il}]$ (e.g. $[M_{11}, M_{22}]=[M_{21}, M_{12}]$). We claim that such matrices behave almost as well as matrices with commutative elements. Namely theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) holds true for them. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and the so--called Cartier-Foata matrices. Also, they enter Talalaev's hep-th/0404153 remarkable formulas: $det(\partial_z-L_{Gaudin}(z))$, det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g in the construction of new generators in $Z(U(\hat{gl_n}))$ (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also discuss applications to the separation of variables problem, new Capelli identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints e.g. in Newton id-s fixed, normal ordering convention turned to standard one, refs. adde

A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory. The differential equation arises as a quantization of a certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and Tsuda.Comment: 15 pages, v2: typos corrected and references added, v3: discussion, appendix and references adde

Integrable Models From Twisted Half Loop Algebras

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaudin magnets, and Calogero-type models of particles on several half-lines meeting at a point.Comment: 22 pages, 1 figure, Introduction improved, References adde

Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

Подготовка медицинского персонала МЧС России к реагированию на радиационные аварии с использованием дистанционного обучения

Despite considerable efforts and significant developments in radiation safety, the risks of radiation incidents in peacetime and wartime remain. Aspects of the ionizing radiation impact on the human body and the clinic of radiation pathology determine the specifics of medical care organization. The most important component of ensuring the readiness of medical institutions and establishments of various ministries and departments to respond to radiation emergencies is the training of medical personnel (health care organizers and doctors of diagnostic and treatment specialty) on radiobiology, clinical radiology, radiation hygiene during the additional professional education (advanced training). The needfor financial and time savings proves the relevance of the use of distance (online) learning technologies. The Institute of Additional Professional Education of the Federal State Budgetary Institution “The Nikiforov Russian Center of Emergency and Radiation Medicine” Ministry of the Russian Federation for Civil Defence, Emergencies and Elimination of Consequences of Natural Disasters has developed the educational program of professional development “Training of medical personnel of EMERCOM of Russia to assist victims of radiation accidents”. The program is included in the System of distance learning of the medical personnel. The program consists of educational and methodical facilities and electronic educational resource, which contain all teaching material and other content to ensure the effective work of students. The main part of the program is implemented remotely with mandatory entrance and intermediate control, and the final on-site part includes seminars, workshops and final certification.Несмотря на значительные усилия и серьезные достижения в обеспечении радиационной безопасности, сохраняются риски возникновения радиационных инцидентов мирного и военного времени. Особенности воздействия ионизирующего излучения на организм человека и клиника лучевой патологии определяют специфику организации медицинской помощи. Важнейшей составляющей обеспечения готовности медицинских учреждений и формирований различных министерств и ведомств к реагированию на чрезвычайные ситуации радиационного характера является подготовка медицинского персонала (организаторов здравоохранения и врачей лечебно-диагностического профиля) по вопросам радиобиологии, клинической радиологии, радиационной гигиены на этапе дополнительного профессионального образования (повышение квалификации). Необходимость экономии финансовых средств и времени обосновывает актуальность применения технологий дистанционного (электронного) обучения. В институте дополнительного профессионального образования Всероссийского центра экстренной и радиационной медицины им. А.М. Никифорова разработана и включена в Систему дистанционного обучения медицинского персонала образовательная программа повышения квалификации «Подготовка медицинского персонала МЧС России к оказанию помощи пострадавшим при радиационных авариях». Программа состоит из учебно-методического комплекса и электронного образовательного ресурса, которые содержат все учебно-методические и информационные материалы для обеспечения эффективной работы слушателей. Основная часть программы реализована дистанционно с обязательным входным и промежуточным контролем, а заключительная очная часть включает семинары, практические занятия и итоговую аттестацию с выдачей удостоверения о повышении квалификации

Тихая эпидемия: Исследование роста проблем психического здоровья в современном обществе

Психическое здоровье — это тема, которая долгое время часто замалчивалась. В этой статье мы рассмотрим основные причины роста психических заболеваний в современном обществе и их влияние на отдельных людей и общество в целом. Мы также рассмотрим некоторые из наиболее эффективных способов решения этой проблемы и обеспечения того, чтобы люди получали помощь, необходимую им для счастливой и здоровой жизни.Mental health is a topic that has often been hushed up for a long time. In this article, we will look at the main causes of the growth of mental illness in modern society and their impact on individuals and society as a whole. We will also look at some of the most effective ways to address this problem and ensure that people receive the help they need to live a happy and healthy life

Transverse-momentum-dependent Multiplicities of Charged Hadrons in Muon-Deuteron Deep Inelastic Scattering

A semi-inclusive measurement of charged hadron multiplicities in deep inelastic muon scattering off an isoscalar target was performed using data collected by the COMPASS Collaboration at CERN. The following kinematic domain is covered by the data: photon virtuality $Q^{2}>1$ (GeV/$c$)$^2$, invariant mass of the hadronic system $W > 5$ GeV/$c^2$, Bjorken scaling variable in the range $0.003 < x < 0.4$, fraction of the virtual photon energy carried by the hadron in the range $0.2 < z < 0.8$, square of the hadron transverse momentum with respect to the virtual photon direction in the range 0.02 (GeV/$c)^2 < P_{\rm{hT}}^{2} < 3$ (GeV/$c$)$^2$. The multiplicities are presented as a function of $P_{\rm{hT}}^{2}$ in three-dimensional bins of $x$, $Q^2$, $z$ and compared to previous semi-inclusive measurements. We explore the small-$P_{\rm{hT}}^{2}$ region, i.e. $P_{\rm{hT}}^{2} < 1$ (GeV/$c$)$^2$, where hadron transverse momenta are expected to arise from non-perturbative effects, and also the domain of larger $P_{\rm{hT}}^{2}$, where contributions from higher-order perturbative QCD are expected to dominate. The multiplicities are fitted using a single-exponential function at small $P_{\rm{hT}}^{2}$ to study the dependence of the average transverse momentum $\langle P_{\rm{hT}}^{2}\rangle$ on $x$, $Q^2$ and $z$. The power-law behaviour of the multiplicities at large $P_{\rm{hT}}^{2}$ is investigated using various functional forms. The fits describe the data reasonably well over the full measured range.Comment: 28 pages, 20 figure