Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence
Quantum Physics
2025-10-07 v2 High Energy Physics - Theory
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 expectation surface areas, perimeters, eccentricities, and shape-parameters. These geometric constants of quantum membranes deviate drastically from classical mechanics.
Keywords
Cite
@article{arxiv.2409.11435,
title = {Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence},
author = {Hai H. Vo and Olivia M. Markowich and Angeline Hu and Nguyen H. Nguyen and Trung V. Phan},
journal= {arXiv preprint arXiv:2409.11435},
year = {2025}
}