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arXiv · hep-th/9911149

On Stable Sector in Supermembrane Matrix Model

I. Ya. Aref'eva·A. S. Koshelev·P. B. Medvedev
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Abstract

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 Schrödinger 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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I. Ya. Aref'eva, A. S. Koshelev, P. B. Medvedev. 1999-11-18. On Stable Sector in Supermembrane Matrix Model. https://doi.org/10.1016/s0550-3213(00)00205-4

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