On Stable Sector in Supermembrane Matrix Model

Details On Stable Sector in Supermembrane Matrix Model On Stable Sector in Supermembrane Matrix Model

1999-11-18

arxiv.org/abs/hep-th/9911149v1

Nucl.Phys. B579 (2000) 411-436

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 5 figures

Scientific paper

10.1016/S0550-3213(00)00205-4

We study the spectrum of SU(2) x SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constraints and single out the quantum number n (the Lorentz angular momentum). Energy levels are four-fold degenerate with respect to n and are labeled by n_q, the largest n in a quartet. The Schr\"odinger equation is reduced to two different systems of two-dimensional partial differential equations. The choice of a system is governed by n_q. We present the asymptotic solutions for the systems deriving thereby the asymptotic formula for the spectrum. Odd n_q are forbidden, for even n_q the spectrum has a continuous part as well as a discrete one, meanwhile for half-integer n_q the spectrum is purely discrete. Taking half-integer n_q one can cure the model from instability caused by the presence of continuous spectrum.

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