{"title":"Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence","authors":"Hai H. Vo, Nguyen H. Nguyen, Trung V. Phan","doi":"arxiv-2409.11435","DOIUrl":null,"url":null,"abstract":"We study the size and shape statistics of ground state fuzzy spheres when\nprojected onto the transverse plane, utilizing the regularized SU(N=2) matrix\nmodel in D=(1+3)-dimensional spacetime. We show that they appear as ellipses,\nfrom matrix/membrane correspondence. With our numerical and analytical\napproximation for the ground state wavefunction, we provide estimations for\ntheir expected surface areas, perimeters, eccentricities, and shape-parameters.\nThese geometric constants of quantum membranes deviate drastically from\nclassical mechanics.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11435","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the size and shape statistics of ground state fuzzy spheres when
projected onto the transverse plane, utilizing the regularized SU(N=2) matrix
model in D=(1+3)-dimensional spacetime. We show that they appear as ellipses,
from matrix/membrane correspondence. With our numerical and analytical
approximation for the ground state wavefunction, we provide estimations for
their expected surface areas, perimeters, eccentricities, and shape-parameters.
These geometric constants of quantum membranes deviate drastically from
classical mechanics.
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