Theoretical analysis reveals elliptical geometries in projected fuzzy spheres, indicating quantum membranes deviate drastically from classical mechanical expectations.
Key Points
To calculate the size and shape characteristics of ground state fuzzy spheres projected onto the transverse plane using matrix/membrane correspondence.
Utilized a regularized SU(N = 2) matrix model in D = (1 + 3)-dimensional spacetime.
Applied numerical and analytical approximation methods to model the ground state wavefunction and derive projected geometric properties.
Demonstrated that fuzzy spheres appear as ellipses when projected onto the transverse plane under matrix/membrane correspondence.
Estimated expected surface areas, perimeters, eccentricities, and shape parameters, showing dramatic deviations from classical geometric predictions.