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Theoretical analysis reveals elliptical geometries in projected fuzzy spheres, indicating quantum membranes deviate drastically from classical mechanical expectations.
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.
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H.T. Vo (2026) studied this question.
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