Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence

• URL: http://arxiv.org/abs/2409.11435v1
• Date: Sun, 15 Sep 2024 16:26:48 GMT
• Title: Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence
• Authors: Hai H. Vo, Nguyen H. Nguyen, Trung V. Phan,
• Abstract summary: We study the size and shape statistics of ground state fuzzy spheres when projected onto the transverse plane. With our numerical and analytical approximation for the ground state wavefunction, we provide estimations for their expected surface areas, perimeters, eccentricities, and shape- parameters.
• Score: 0.10923877073891444
• License: http://creativecommons.org/licenses/by/4.0/
• 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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