相关论文: Normal operators for momentum ray transforms, I: T…

We apply the Effective Field Theory approach to General Relativity, introduced by Goldberger and Rothstein, to study point-like and string-like sources in the context of scalar-tensor theories of gravity. Within this framework we compute…

We summarize recent non-perturbative results obtained for the renormalization constants computed in the RI'-MOM scheme for $N_{\rm f}=2+1+1$ twisted mass QCD. Our implementation employs the Iwasaki gauge action and four dynamical degenerate…

Starting from the irreducible representations of the group of the wave vector we construct the spin wave functions consistent with inversion symmetry, neglected in the usual representation analysis. We obtain the relation between the basis…

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the…

In coupled rotor models which describe identical rotating nuclei the nuclear spin states restrict the possible angular momenta of each molecule. There are two mean-field approaches to determining the orientational phase diagrams in such…

Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…

This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging. An expansion scheme for the pseudodifferential symbol of the…

The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…

The integral operator of the form $$\bigl(Nu\bigr)(x)=\sum_{k=1}^\infty e^{i\langle\omega_k,x\rangle} \int_{\mathbb R^c}n_k(x-y)\,u(y)\,dy$$ acting in $L_p(\mathbb R^c)$, $1\le p\le\infty$, is considered. It is assumed that…

Using the methods of the 'form factor program' exact expressions of all matrix elements are obtained for several operators of the quantum sine-Gordon model alias the massive Thirring model. A general formula is presented which provides form…

The Minkowski tensors are the natural tensor-valued generalizations of the intrinsic volumes of convex bodies. We prove two complete sets of integral geometric formulae, so called kinematic and Crofton formulae, for these Minkowski tensors.…

The typical transverse momentum of a quark in the proton is a basic property of any QCD based model of nucleon structure. However, calculations in phenomenological models typically give rather small values of transverse momenta, which are…

We give a gauge-invariant treatment of the angular momentum sum-rule for the proton in terms of matrix elements of three gauge-invariant, local composite operators. These matrix elements are decomposed into three independent form factors,…

In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have…

We study perturbative renormalization of the composite operators in the $T\bar T$-deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases.…

The formalism of linear response theory for Skyrme forces including tensor terms presented in article [1] is generalized for the case of a Skyrme energy density functional in infinite matter. We also present analytical results for the…

Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete,…

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all…

Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most…

In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $\mathbb{R}^2$. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the…