Chiral moments make chiral measures

Fuente: arXiv
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Main Authors: Pisanty, Emilio, Mayer, Nicola, Ordóñez, Andrés, Löhr, Alexander, Khokhlova, Margarita
Format: Preprint
Published: 2026
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author Pisanty, Emilio
Mayer, Nicola
Ordóñez, Andrés
Löhr, Alexander
Khokhlova, Margarita
author_facet Pisanty, Emilio
Mayer, Nicola
Ordóñez, Andrés
Löhr, Alexander
Khokhlova, Margarita
contents We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only via its angular shape consistently with existing multipolar-moment approaches, but also its radial dependence. We combine these tensorial moments into a rotationally-invariant pseudoscalar using a newly-defined cross product and triple product for arbitrary symmetric tensors. We analyze these measures for a variety of toy-model distributions, providing intuition for the geometry and guiding the choice of chiral measure optimal for a given distribution. We also apply our measures to a physically-motivated example coming from photoionization in polychromatic chiral light. Our work provides a robust, flexible, intuitive, highly geometrical, and physically-driven framework for understanding and quantifying the chirality of a wide variety of distributions, together with an open-source software package that makes this toolbox readily applicable for the analysis of numerical or experimental data.
format Preprint
id arxiv_https___arxiv_org_abs_2603_26793
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Chiral moments make chiral measures
Pisanty, Emilio
Mayer, Nicola
Ordóñez, Andrés
Löhr, Alexander
Khokhlova, Margarita
Data Analysis, Statistics and Probability
Optics
Quantum Physics
We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only via its angular shape consistently with existing multipolar-moment approaches, but also its radial dependence. We combine these tensorial moments into a rotationally-invariant pseudoscalar using a newly-defined cross product and triple product for arbitrary symmetric tensors. We analyze these measures for a variety of toy-model distributions, providing intuition for the geometry and guiding the choice of chiral measure optimal for a given distribution. We also apply our measures to a physically-motivated example coming from photoionization in polychromatic chiral light. Our work provides a robust, flexible, intuitive, highly geometrical, and physically-driven framework for understanding and quantifying the chirality of a wide variety of distributions, together with an open-source software package that makes this toolbox readily applicable for the analysis of numerical or experimental data.
title Chiral moments make chiral measures
topic Data Analysis, Statistics and Probability
Optics
Quantum Physics
url https://arxiv.org/abs/2603.26793