arXiv subjects

I. V. Anikin

Publications and source records attributed to I. V. Anikin.

At least 19 recordsLinked to original sources

arXiv2026

Non-integral geometry: additional term $f_A$ as a regularizing term

In the present paper, we first describe the principal basis of non-integral geometry. Non-integral geometry is a new field of generalized function (distribution) theory where the effects breaking the symmetry of integration measure have been investigated. In turn, the non-symmetric integration measure (the non-invariant measure) leads to the complex form of the universal, dimension-independent inverse operator with the additional contributions compared to the methods of integral geometry. The additional term with the complex integration measure serves to the extension that improves the image reconstruction procedure. Then, we prove that this additional term $f_A$ in the universal inverse Radon transforms plays a role of the regularizing contribution. In particular, we show that owing to the presence of $f_A$ the corresponding complex singularities can be eliminated in the image reconstruction process.

hep-th↗

arXiv2025

Complexity of Radon transforms

For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized functions, if the outset (origin) function which generates the Radon image is a pure-real function, as a rule, the complexity of Radon transforms becomes in question. In the paper, we discuss the Fourier slice theorem analyzing the degenerated (singular) points as possible sources of the complexity. We also demonstrate the different methods to generate the needed complexity on the intermediate stage of calculations. Besides, we show that the introduction of the hybrid (Wigner-like) function ensures naturally the corresponding complexity. The discussed complexity provides not only the additional contribution to the inverse Radon transforms, but also it makes an essential impact on the reconstruction and optimization procedures within the frame of the incorrect problems. The presented methods can be effectively used for the practical tasks of reconstruction problems.

math.FA↗

arXiv2025

Universal inverse Radon transforms: Inhomogeneity, angular restrictions and boundary

An alternative method to invert the Radon transforms without the use of Courant-Hilbert's identities has been proposed and developed independently from the space dimension. For the universal representation of inverse Radon transform, we study the consequences of inhomogeneity of outset function without the restrictions on the angular Radon coordinates. We show that this inhomogeneity yields a natural evidence for the presence of the extra contributions in the case of the full angular region. In addition, if the outset function is well-localized in the space, we demonstrate that the corresponding boundary conditions and the angular restrictions should be applied for both the direct and inverse Radon transforms. Besides, we relate the angular restrictions on the Radon variable to the boundary exclusion of outset function and its Radon image.

math.CA↗

arXiv2025

TMD-like functions through the twisted quark states

We investigate a new class of transverse momentum dependent functions (TMDs), as known as align-spin (AS) functions. In the paper, we propose the most suitable proof of the AS-function existence together with the demonstration of the preponderances if the framework of twisted quark states has been employed. The twisted state corresponds to the elementary particle (quark) which possesses the nontrivial intrinsic orbital angular momentum owing to the swirling trajectory of motion. In its turn, it leads to the cylindric system applied for the consideration. In this connection, we reveal that the twisted (vortex) quark states serve as effective tools for the study of TMDs, thereby facilitating a comprehensive analysis of AS-functions. In contrast to the previous studies, where the existence of new TMDs is related to the the corresponding interactions encoded in the correlators, we now focus on the leading order of interactions providing a simplified and robust method. This has been ensured by the twisted quark in the corresponding correlator because the essential transverse momentum dependence of quarks generated by interactions in the correlators can be alternatively described by the twisted states. Using a cylindrical formulation for twisted states, we can combine the properties of plane-wave particles with a description stemmed from spherical harmonics, resulting in well-defined propagation directions accompanied by essential OAM projections. In particular, this innovative framework opens a new window for the direct investigations of AS-functions, generating the unique angular $ϕ$-dependence of differential cross sections. It also points towards promising applications in experimental particle physics.

hep-ph↗

arXiv2024

Inverse Radon transforms: analytical and Tikhonov-like regularizations of inversion

We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new analytical term to the Tikhonov regularization of Moore-Penrose's inversion procedure, we derive new optimization conditions that extend the Tikhonov regularization framework and influence the fitting parameter. This enhancement yields a more robust and accurate reconstruction of physical quantities, demonstrating its potential impact on various studies. We illustrate the significance of new term through schematic examples of physical applications, highlighting its relevance to diverse fields. Our findings provide a valuable tool for improving inversion methods and their applications in physics and beyond.

physics.comp-ph↗

arXiv2024

Contour gauge: Compendium of Results in Theory and Applications

In this review, we outline the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in $SU(3)$ gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields.

hep-ph↗

arXiv2023

Conformal Symmetry and Effective Potential: II. Evolution

We present the second part of a paper series devoted to the study of the multi-loop effective potential evolution in $φ^4$-theory using the conformal symmetry. In this paper, we demonstrate that the conformal symmetry can still be useful for the effective potential approach even at the presence of the mass parameter. To this goal, it is necessary to introduce the special treatment of the mass terms as sorts of interaction in an asymptotical expansion of the generating functional. The introduced vacuum $V_{z,x}$-operation is the main tool to the algebraic scheme of anomalous dimension calculations. It is shown that the vacuum $V_{z,x}$-operation transforms the given Green functions to the corresponding vacuum integrations which generate the effective potential.

hep-ph↗

arXiv2023

The Gorishny-Isaev vacuum integrations and UV(IR)-regime

We present the further development of the vacuum massless integrations. In particular, in the Gorishny-Isaev formula, it has been shown that the delta function representing UV-regime should be treated within the sequential approach. It allows us to resolve the problem of vacuum integrations related to the analytical continuation of diagram indices.

hep-ph↗

arXiv2023

Conformal Symmetry and Effective Potential: I. Vacuum $V_{z,x}$-operation for the Green functions

We begin a series of two papers that is devoted to the study of the multi-loop effective potential evolution in $φ^4$-theory using the conformal symmetry. In the first part, we introduce and describe in detail the vacuum $V_{z,x}$-operation ($"V"$ stems from "vacuum", $\{z,x\}$ imply the corresponding coordinates) that transforms the given Green functions to the corresponding vacuum integrations which generate the effective potential. Our operation can be considered as an inverse procedure compared to the Gorishni-Isaev method. To the final goal, it is necessary to introduce also the special treatment of the mass terms as sorts of "interaction" in an asymptotical expansion of the generating functional.

hep-ph↗

arXiv2023

Vacuum Integration: UV- and IR-divergencies

In this note we present the important details regarding the massless vacuum integrations which are not outlined in the literature. In particular, it has been shown how the delta-function represents either UV-regime or IR-regime. In the case of vacuum integration, we advocate the use of sequential approach to the singular generated functions (distributions). The sequential approach is extremely useful for many practical applications, in particular, in the effective potential method.

hep-ph↗

arXiv2022

Archetypal Factorization and Gluon Poles in semi-exclusive reactions

Within the archetypal factorization procedure, we study the gluon pole contributions manifesting in the nucleon-lepton hard processes of hadron production. We prove the dominant role of gluon pole contributions in the processes of such kind. We analyse the different sources of complexity associated with the gluon pole functions. As a practical application, we derive a new single spin asymmetry related directly to the gluon poles which can be studied experimentally.

hep-ph↗

arXiv2022

On new $k_\perp$-dependent (quasi)parton distribution functions

We advocate the existence of a new type of $k_\perp$-dependent functions. In contrast to the well-known Boer-Mulders function, the presented new functions can be associated with the collective alignment of quark spin vectors. Moreover, the new functions are sensitive to the transverse motion of partons inside hadrons, which are linked to the spin alignment of partons, and they are initiated by the interactions encoded in the corresponding correlators.

hep-ph↗

arXiv2022

Parton distributions: Functional complexity and Lorentz parametrization

In the paper we focus on the study of the functional complexity of the Lorentz parametrizing functions in connection with the time-reversal transformations. We argue that the interactions encoded in the corresponding correlators of non-local quark(-gluon) operators generate additional sources of functional complexity for the parametrizing functions which are not discussed in the literature. We also revisit the Lorentz parametrization of different correlators given by the hadron matrix elements of the non-local operators. The evidences for the new parametrizing function existence have been presented.

hep-ph↗

arXiv2022

Alignment function as a new kind of transverse momentum dependent functions

We argue the existence of new $k_\perp$-dependent functions which can be manifested in the Drell-Yan (SIDIS)-like processes. The presented new functions resemble the well-known Boer-Mulders function associated with the quark spin asymmetry, but in contrast they are sensitive to the transverse motion of partons inside the hadron due to the collective alignment of quark spin vectors.

hep-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

The contour gauge in use: telling untold

In Quantum Field Theory, we discuss the main features of the (non-local) contour gauge which extends the local axial-type gauge used in most approaches. Based on the gluon geometry, we demonstrate that the contour gauge does not suffer from the residual gauge. We discuss the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. Having compared the local and non-local gauges, we again advocate the advantage of the contour gauge use.

hep-ph↗

arXiv2021

On the decomposition theorem for gluons

Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. $A_μ= A_μ^{\text{phys}}+A_μ^{\text{pure}}$. In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided the contour gauge condition.

hep-ph↗

arXiv2021

On vacuum integration

The effective potential is known to be given by the vacuum diagrams. In this paper we show that the massive loop integrations corresponding to the vacuum diagrams can be expressed through the massless loop integrations with the corresponding massive prefactor provided the special treatment of $δ(0)$-singularity. In its turn, the massless loop integrations provide the useful instrument for the conformal symmetry application.

hep-ph↗