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A. A. Vladimirov

Publications and source records attributed to A. A. Vladimirov.

At least 55 records · Page 3Linked to original sources
arXiv2010

Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.

hep-ph↗
arXiv2009

Dynamic spin susceptibility in the t-J model

A relaxation-function theory for the dynamic spin susceptibility in the $t$--$J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperaturs. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on La_{2-δ}Sr_δ)CuO_4. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its (ω/T) scaling behavior are calculated in a reasonable agreement with experimental and ED data.

cond-mat.str-el↗
arXiv2009

Leading Chiral Logarithms for Pion Form Factors to Arbitrary Number of Loops

We develop the method of calculation of the leading chiral (infrared) logarithms to an arbitrary loop order for various form factors of Nambu-Goldstone bosons. The method is illustrated on example of scalar and vector form factors in massless 4D O(N+1)/O(N) sigma-model. The analytical properties of the form factors are derived. The leading chiral (infrared) logarithms are summed up in the large N limit.

hep-ph↗
arXiv2008

On the Chebyshev properties of system of eigenfunctions for Sturm--Liouville problem with singular coefficients

In the paper we consider singular spectral Sturm--Liouville problem $-(py')'+(q-λr)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function $p\in L_{\infty}[0,1]$ is uniformly positive, generalized function $q\in W_2^{-1}[0,1]$ is real-valued, generalized weight function $r\in W_2^{-1}[0,1]$ is positive and unitary matrix $U\in\mathbb C^{2\times 2}$ is diagonal. The goal is to prove that well-known (for smooth case) facts about Chebyshev property of eigenfunctions hold in general case.

math.SP↗
arXiv2008

On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients

In the paper we consider singular spectral Sturm--Liouville problem $-(py')'+(q-λr)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function $p\in L_{\infty}[0,1]$ is uniformly positive, generalized functions $q,r\in W_2^{-1}[0,1]$ are real-valued and unitary matrix $U\in\mathbb C^{2\times 2}$ is diagonal. The main goal is to prove that well-known (for smooth case) facts about number and distribution of zeros of eigenfunctions hold in general case.

math.SP↗
arXiv2008

Unitarization of elastic amplitude on SO_mu(2.1) group

We obtain the solution of the unitarity equation for the elastic processes in terms of the expansion coefficients of the amplitude as a function on the SO_mu(2.1) group. This approach is a generalization of the eikonal representation to the case of small impact parameters and large transverse momenta. We show how the unitarity relation is modified when the contributions of the backward scattering are taken into account. We discuss the simplest models of the profile functions in the following cases: full reflection, full absorption and the combination of these two cases.

hep-ph↗
arXiv2008

Spatial image of reaction area from scattering I: SO_mu(2.1) algebra formalism

We develop general formalism of how to relate scattering amplitudes for exclusive processes to spatial image of target hadron. More precisely we show how to determine the spatial distribution of outgoing particles in the space of so-called nearest approach parameter. This parameter characterizes the position in the coordinate space the place where the final particle is produced.

hep-ph↗
arXiv2008

Spatial image of reaction area from scattering.II: On connection between the differential cross-sections in transverse momentum and in nearest approach parameter

We develop general formalism of how to relate cross-section for exclusive processes to spatial image of reaction area. More precisely we show how to determine the spatial distribution of outgoing particles in the space of so-called nearest approach parameter. This parameter characterizes the position in the coordinate space the place where the final particle is produced.

hep-ph↗
arXiv2007

On a continuity theorem for constructive functions

One proves that any everywhere defined constructive mapping from a complete metric space into a complete metric space which preserves the property of precompacity of subsets is locally uniformly continuous. This fact can be viewed as interpretation of L. E. J. Brower's fan theorem in terms of A. A. Markov's constructive analysis.

math.LO↗
arXiv2004

Lectures on integrable hierarchies and vertex operators

This is a write-up of lectures intended for (under)graduate students. Contents: Scalar Ansatz (KP hierarchy). Fermionic Fock space. Fermi-Bose correspondence. KP hierarchy via free fermions. Formal distributions and locality. Operator product expansion. Vertex algebras. Free fermions. Virasoro algebra in KdV.

hep-th↗
arXiv2003

The estimates for the number of the eigenvalues of abstract and differential operator functions

We consider an operator function (F(λ)) for (λ\in(σ,τ)\subseteq\mathbb R) whose values are semibounded selfadjoint operators in Hilbert space (\mathfrak H). Our main goal is to estimate the number (\mathcal N_F(α,β)) of the eigenvalues of (F(λ)) on a segment ([α,β)\Subset(σ,τ)). In particular, we prove the estimates (\mathcal N_F(α,β)\geqslant ν_F(β)-ν_F(α)) and (\mathcal N_F(α,β)= ν_F(β)-ν_F(α)) where (ν(ξ)) is the number of the negative eigenvalues of the operator (F(ξ)), (ξ\in(σ,τ)). The obtained results are applied for the functions of ordinary differential operators on a finite interval.

math.FA↗
arXiv1997

On the algebraic structure of differential calculus on quantum groups

Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups -- coordinate functions, differential 1-forms, Lie derivatives, and inner derivations -- as the cross-product algebra of two mutually dual graded Hopf algebras. This construction, properly taking into account Hopf-algebraic properties of Woronowicz's bicovariant calculus, provides a direct proof of the Cartan identity and of many other useful relations. A detailed comparison with other approaches is also given.

q-alg↗