Chiral moments make chiral measures
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918413515882496 |
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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 |