On Lorentz invariance of the quantum membrane

Abstract

We study the $SO\left(2\right)\times SU(N=2)$ invariant matrix models corresponding to the regularised description of the quantum bosonic membrane in $D=4$ dimensional spacetime. The lowest energy levels and the wave function of the ground state are computed numerically with satisfactory accuracy. We observe an approximate degeneracy of energy levels required by Lorentz invariance of the $N\to \infty$ theory.