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A. V. Ivanov

Publications and source records attributed to A. V. Ivanov.

At least 37 records · Page 2Linked to original sources
arXiv2022

Formula for two-loop divergent part of 4-D Yang-Mills effective action

In the paper, we study the two-loop contribution to the effective action of the four-dimensional quantum Yang-Mills theory. We derive a new formula for the contribution in terms of three functions, formed from the Green's function expansion near the diagonal. This result can be applied to different types of regularization. Therefore, we test it by using the dimensional regularization and cutoff ones and show the consistence with the results, obtained in other works.

hep-th↗
arXiv2022

Special Functions for Heat Kernel Expansion

In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley-DeWitt coefficients of this decomposition satisfy a set of recurrence relations, which we use to construct two function families of a special kind. Using these functions, we study the expansion of a local heat kernel for the inverse Laplace operator. We show that the new functions have some important properties. For example, we can consider the Laplace operator on the function set as a shift one. Also we describe various applications useful in theoretical physics and, in particular, we find a decomposition of Green's functions near the diagonal in terms of new functions.

math-ph↗
arXiv2022

Conceptual design of the Spin Physics Detector

The Spin Physics Detector, a universal facility for studying the nucleon spin structure and other spin-related phenomena with polarized proton and deuteron beams, is proposed to be placed in one of the two interaction points of the NICA collider that is under construction at the Joint Institute for Nuclear Research (Dubna, Russia). At the heart of the project there is huge experience with polarized beams at JINR. The main objective of the proposed experiment is the comprehensive study of the unpolarized and polarized gluon content of the nucleon. Spin measurements at the Spin Physics Detector at the NICA collider have bright perspectives to make a unique contribution and challenge our understanding of the spin structure of the nucleon. In this document the Conceptual Design of the Spin Physics Detector is presented.

hep-ex↗
arXiv2021

Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals

Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase $θ$ on the fermions. We establish main properties of the spectral functions which ensure applicability of the $ζ$ function regularization and of the usual heat kernel formulae for chiral and parity anomalies. We develop computational methods, including a perturbation expansion for the heat kernel. We show that the terms in both anomalies which include electromagnetic potential are independent of $θ$.

math-ph↗
arXiv2021

Some Basic Tools of QFT

This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such concepts as the functional integral, the generating functions, the background field method and the Feynman diagram technique, and also consider relations among them. The model under consideration allows us to perform all the calculations explicitly, which significantly increases the visibility and clarity of the notes. We also provide neat proofs that are usually omitted in standard educational publications.

hep-th↗
arXiv2021

Index Theorem for Domain Walls

The paper is devoted to the discussion of index theorem for domain walls condition. We give an extension of the theorem to the case, when not only Yang-Mills connection components have a jump on some surface of co-dimension 1, but also components of a Riemannian connection, while a metric remains continuous.

math-ph↗
arXiv2020

Two-Loop Cutoff Renormalization of 4-D Yang-Mills Effective Action

In the paper we study the Yang-Mills effective action in the four-dimensional space-time by using background field formalism. We give an explicit way of cutoff regularization procedure, then do a two-loop renormalization and calculate a second $β$-function coefficient. We also show that the two-loop singularity contains only logarithmic part in the first degree. At the same time additional properties of a Green function regular part are obtained.

hep-th↗
arXiv2020

Atiyah-Patodi-Singer Index Theorem for Domain Walls

We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection jumps. We formulate and prove an analog of the Atiyah-Patodi-Singer theorem that relates the index to the bulk integral of Pontryagin density and $η$-invariants of auxiliary Dirac operators on the domain wall. Thus the index is expressed through the global chiral anomaly in the volume and the parity anomaly on the wall.

math-ph↗
arXiv2020

Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson line

The proper time method plays an important role in modern mathematics and physics. It includes many approaches, each of which has its pros and cons. This work is devoted to the description of one model case, which reflects the subtleties of construction and can be extended to a more general cases (curved space, manifold with boundary), and contains two interrelated parts: asymptotic expansion and path intergal representation. The paper discusses in details the importance of gauge conditions and role of the ordered exponentials, gives the proof of a new non-recursive formula for the Seeley-DeWitt coefficients on the diagonal, as well as the equivalence of the two main approaches using the exponential formula.

hep-th↗
arXiv2018

Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts

We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such that $f^{-1}(y)$ is metrizable for all $y\in Y$ . A continuous map of compacts $f : X \to Y$ is said to be fully closed if for any disjoint closed subsets $A;B \subset X$ the intersection $f(A) \cap f(B)$ is finite. For instance the projection of the lexicographic square onto the first factor is fully closed and all its fibers are homeomorphic to the closed interval.

math.FA↗
arXiv2015

Laser spectroscopy of finite size and covering effects in magnetite nanoparticles

The experiments on the impact of the size of magnetite clusters on various magnetic properties (magnetic moment, Curie temperature, blocking temperature etc.) have been carried out. The methods of magnetic separation, centrifuging of water suspensions of biocompatible iron oxide nanoparticles (NPs) allow producing fractions with diameter of nanoparticles in the range of 4÷22 nm. The size of NPs are controlled by the methods of dynamic light scattering (DLS), transmission electron microscopy (TEM) and atomic force microscopy (AFM). For the first time the DLS method is applied in real time to control the size during the process of the separation of the NPs in aqueous suspensions. The changes of the size of NPs cause a shift in the Curie temperature and in the changes in the specific magnetic properties of the iron NPs. The experimental data is interpreted on the basis of Monte Carlo simulations for the classical Heisenberg model with different bulk and surface magnetic moments. It is demonstrated experimentally and by theoretical modeling that magnetic properties of magnetite NPs are determined not only by their sizes, but also by the their surface spin states, while both growing and falling dependences of the magnetic moment (per Fe3O4 formula unit) being possible, depending on the number of magnetic atoms in the nanoparticle. Both NPs clean and covered with a bioresorbable layer clusters have been investigated.

cond-mat.mtrl-sci↗
arXiv2015

Energy surface and minimum energy paths for Fréedericksz transitions in bistable cholesteric liquid crystals

The multidimensional energy surface of a cholesteric liquid crystal in a planar cell is investigated as a function of spherical coordinates determining the director orientation. Minima on the energy surface correspond to the stable states with particular director distribution. External electric and magnetic fields deform the energy surface and positions of minima. It can lead to the transitions between states, known as the Fréedericksz effect. Transitions can be continuous or discontinuous depending on parameters of the liquid crystal which determine an energy surface. In a case of discontinuous transition when a barrier between stable states is comparable with the thermal energy, the activation transitions may occur and it leads to the modification of characteristics of the Fréedericksz effect with temperature without explicit temperature dependencies of liquid crystal parameters. Minimum energy path between stable states on the energy surface for the Fréedericksz transition is found using geodesic nudged elastic band method. Knowledge of this path, which has maximal statistical weight among all other paths, gives the information about a barrier between stable states and configuration of director orientation during the transition. It also allows one to estimate the stability of states with respect to the thermal fluctuations and their lifetime when the system is close to the Fréedericksz transition.

cond-mat.soft↗
arXiv2009

Heat flow of the Earth and resonant capture of solar 57-Fe axions

In a very conservative approach, supposing that total heat flow of the Earth is exclusively due to resonant capture inside the Earth of axions, emitted by 57-Fe nuclei on Sun, we obtain limit on mass of hadronic axion: m_a<1.8 keV. Taking into account release of heat from decays of 40-K, 232-Th, 238-U inside the Earth, this estimation could be improved to the value: m_a<1.6 keV. Both the values are less restrictive than limits set in devoted experiments to search for 57-Fe axions (m_a<216-745 eV), but are much better than limits obtained in experiments with 83-Kr (m_a<5.5 keV) and 7-Li (m_a<13.9-32 keV).

nucl-ex↗