Related papers: Locally-smeared operator product expansions
In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon…
Some basic concepts are discussed to derive renormalisation factors of local lattice operators relevant to deep inelastic structure functions and to other measurable quantities. These $Z$ factors can be used to relate matrix elements…
I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the…
In this work we provide a massless perturbative framework for the two dimensional non-linear sigma model (NLSM), that allows the computation of the perturbative series attached to the operator condensates in the operator product expansion…
Self-Organizing Maps (SOM) are a classical method for unsupervised learning, vector quantization, and topographic mapping of high-dimensional data. However, existing SOM formulations often involve a trade-off between computational…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
Rotary Position Embedding (RoPE) has become a core component of modern Transformer architectures across language, vision, and 3D domains. However, existing implementations rely on vector-level split and merge operations that introduce…
We propose a nonlocal operator method for solving partial differential equations (PDEs). The nonlocal operator is derived from the Taylor series expansion of the unknown field, and can be regarded as the integral form "equivalent" to the…
We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with…
We show, within the framework of the Euclidean $\phi^4$-quantum field theory in four dimensions, that the Wilson operator product expansion (OPE) is not only an asymptotic expansion at short distances as previously believed, but even…
Machine Learning Interatomic Potentials (MLIPs) enable accurate large-scale atomistic simulations, yet improving their expressive capacity efficiently remains challenging. Here we systematically develop Mixture-of-Experts (MoE) and…
The operator product expansion (OPE) in 4d (super)conformal field theory is of broad interest, for both formal and phenomenological applications. In this paper, we use conformal perturbation theory to study the OPE of nearly-free fields…
Deep inelastic scattering of $\mathcal{R}$-currents and the scattering of a small dipole on finite length hot $\mathcal{N}=4$ SYM matter are discussed. In each case we find the scale when scattering becomes strong is determined by a…
Hadronic matrix elements evaluated on the lattice can be converted to a continuum scheme such as $\MSbar$ using intermediate non-perturbative renormalisation schemes. Discretisation effects on the lattice and convergence of the continuum…
We present an algorithmic construction scheme for matrix-product-operator (MPO) representations of arbitrary $U(1)$-invariant operators whenever there is an expression of the local structure in terms of a finite-states machine (FSM). Given…
In deep reinforcement learning (DRL), an agent is trained from a stream of experience. In a continual learning setting, such agents can suffer from plasticity loss: their ability to learn new skills from new experiences diminishes over…
Rotary Position Embedding (RoPE) is widely adopted in large language models (LLMs) due to its efficient encoding of relative positions with strong extrapolation capabilities. However, while its application in higher-dimensional input…
Operator product expansion (OPE) of two operators in two-dimensional conformal field theory includes a sum over Virasoro descendants of other operator with universal coefficients, dictated exclusively by properties of the Virasoro algebra…