Related papers: opbasis -- a Python package to derive minimal oper…
In this paper we present a short overview of the new Wolfram Mathematica package intended for elementary "in-basis" tensor and differential-geometric calculations. In contrast to alternatives our package is designed to be easy-to-use,…
Mapping UV theories onto low energy effective descriptions is a procedure known as matching. The last decade has seen tremendous progress in the development of new tools for efficiently performing matching calculations, by relying on…
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…
We consider the O(3) or CP(1) nonlinear sigma model as an effective field theory in a derivative expansion, with the most general Lagrangian that obeys O(3), parity and Lorentz symmetry. We work out the complete list of possible operators…
We present a systematic method for constructing lattice QCD operators for systems of an arbitrary number of particles with arbitrary momentum, spin, and internal quantum numbers. Explicit constructions are provided for one-, two-, three-,…
We present a minimal basis for non-derivative baryon-number-violating operators in the Standard Model Effective Field Theory up to mass dimension 11, as well as for the $(\Delta B,\Delta L) = (2,2)$ and $(2,-2)$ operators at dimension 12.…
Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also…
We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix…
Machine learning techniques have been paramount throughout the last years, being applied in a wide range of tasks, such as classification, object recognition, person identification, and image segmentation. Nevertheless, conventional…
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided…
We propose an operator preconditioner for general elliptic pseudodifferential equations in a domain $\Omega$, where $\Omega$ is either in $\mathbb{R}^n$ or in a Riemannian manifold. For linear systems of equations arising from low-order…
As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
A version of Gabor expansion over a lattice of critical density is shown to converge to an arbitrary function that belongs to domain of the oscillator operator. This expansion is used for approximation of an arbitrary function concentrated…
According to the modern paradigms of software engineering, standard tasks are best accomplished by reusable open source libraries. We describe OpenOrbitalOptimizer: a reusable open source C++ library for the iterative solution of coupled…
In this paper, we explain how perturbative quantum field theory can be formulated in terms of (a version of) vertex algebras. Our starting point is the Wilson-Zimmermann operator product expansion (OPE). Following ideas of a previous paper…
Subspaces obtained by the orthogonal projection of locally supported square-integrable vector fields onto the Hardy spaces $H_+(\mathbb{S})$ and $H_-(\mathbb{S})$, respectively, play a role in various inverse potential field problems since…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…
Focused optical fields are key to a multitude of applications involving light-matter interactions, such as optical microscopy, single-molecule spectroscopy, optical tweezers, lithography, or quantum coherent control. A detailed vectorial…