标题： 弦比特的超对称量子力学 显示英文标题

标题： Supersymmetric Quantum Mechanics for String-Bits

摘要： 我们发展了可能的超对称单粒子量子力学版本，同时着眼于将其应用于超弦比特模型。 我们主要关注空间维度为$d=1,2,4,8$的情况，这是超弦在$3,4,6,10$维时空中的横向维数。 这些情况是“经典”超弦有意义的情形，也是胡克定律与最简单超粒子动力学相容的$d$值。 我们要解决的基本问题是：何时可以用更一般的力代替这些谐波力，包括在大距离处消失的力？ 这是一个重要的问题，因为不随距离衰减的弦比特之间的力几乎肯定会破坏聚类分解。 我们证明了对于$d=1,2$情况答案是肯定的，对于$d=8$是否定的，而$d=4$目前尚无定论。 显示英文摘要

摘要： We develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions $d=1,2,4,8$, the transverse dimensionalities of superstring in $3,4,6,10$ space-time dimensions. These are the cases for which ``classical'' superstring makes sense, and also the values of $d$ for which Hooke's force law is compatible with the simplest superparticle dynamics. The basic question we address is: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for $d=1,2$, negative for $d=8$, and so far inconclusive for $d=4$.