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N. V. Kharuk

Publications and source records attributed to N. V. Kharuk.

13 recordsLinked to original sources
arXiv2026

On background fields and a cutoff in sigma models

In this paper, using the example of a two-dimensional nonlinear sigma model with the Heisenberg group, we compare two variants of chiral field decomposition into a background part and a fluctuation. It is shown that only one of these methods is consistent with the construction of the generating functional by introducing a background field. Furthermore, we perform a one-loop renormalization of the quantum action, calculate power-law singularities in the two-loop approximation, and consider transition to an extended classical action. Finally, we study the consistency of the cutoff with special functional relations within the framework of the background field method.

hep-th↗
arXiv2026

Renormalization aspects of the Yang-Mills theory with a cutoff

The paper discusses renormalization aspects of the quantum four-dimensional Yang-Mills theory with a cutoff regularization in the coordinate representation. The background field method is used to formulate a generating functional, and the regularization is introduced through quasi-local probabilistic averaging. Two main types of regularization are proposed: strong deformation, which consists in averaging fluctuation fields, and weak deformation, which is a covariant generalization of the first case with respect to gauge transformations of the background field. We study singular contributions for the first two quantum corrections in this paper and compare them in detail with the case of dimensional regularization. The consistency of the action and the equation of motion after introducing the regularization and making a renormalization procedure is analyzed. New counter-vertices are studied, in particular their locality properties and dependence on the regularization parameter.

hep-th↗
arXiv2025

Four-loop renormalization with a cutoff in a sextic model

The quantum action for a three-dimensional real sextic model using the background field method is considered. Four-loop renormalization of this model is performed with a cutoff regularization in the coordinate representation. The coefficients for the renormalization constants are found, the applicability of the $\mathcal{R}$-operation within the proposed regularization is explicitly demonstrated, and the absence of nonlocal contributions is proved. Additionally, the explicit form of the singularities, power and logarithmic, as well as their dependence on the deformation of the Green's function are discussed.

hep-th↗
arXiv2024

Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization

The paper studies the quantum action for the five-dimensional real $ϕ^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed.

hep-th↗
arXiv2023

Ordered Exponential and Its Features in Yang-Mills Effective Action

In this paper we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds. As an example of application, we study a dependence of the four-dimensional quantum Yang-Mills effective action on the background filed and gauge transformations. Also, we formulate some open questions about a structure of divergences.

hep-th↗
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↗
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

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

Modifying the theory of gravity by changing independent variables

We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with electromagnetic potential. The methods of adding matter in the form of scalar and spinor fields are studied. In particular, the expansion of the local symmetry group up to $GL(2,C)$ is explored, in which equations of Einstein, Maxwell and Dirac are reproduced for the theory with Weyl spinor.

gr-qc↗
arXiv2018

Description of gravity in the model with independent nonsymmetric connection

A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result of variation with respect to the metric Einstein equations are obtained. A variation with respect to the connection leads to an arbitrariness in the determination of connection, i.e. the presence of gauge invariance. Then a matter in a form of point particle which interacts with field of connection is introduced. Also the action is complemented by a kinetic term for field of the connection to avoid incompatible equation of motion. Thus after the variation procedures we obtain the Einstein equations, the geodesic equation and the Maxwell`s equations for electromagnetism, where some components of the connection play the role of the electromagnetic potential. Thereby the electromagnetic potential is obtained from the geometry of space-time.

gr-qc↗
arXiv2017

Classical electromagnetic potential as a part of gravitational connection: ideas and history

We consider a natural form of unified theory of gravity and electromagnetism which was somehow missed at the time of intense search for such an unification, and was noticed only in 1978 but remained quite unknown. The basic idea of this unification is to use the metric and non-symmetric connection as independent variables, which generalizes the so-called Palatini formalism. The certain components of connection in the appearing theory can be naturally identified with electromagnetic potential, and with the proper choice of action the Einstein-Maxwell equations are reproducing. In this paper we compare such an approach with the known ideas of unification. Also we propose the more consistent way of including matter (in the form of classical particles) in the theory and briefly discuss the perspectives of further development of this approach.

gr-qc↗