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Woit · 2025-10-20
已登记出处中的最早位置：§33 · zh-CN。
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§33 · zh-CN · machine_draft · machine-draft-not-reviewed
玻色子系统与费米子系统的态空间上分别有来自李代数或李超代数表示的算符。把两个系统作张量积后，这些算符仍作用于组合系统。在某些特殊情形下，还会出现混合玻色子与费米子、并与哈密顿量对易的新算符，通常可看作哈密顿量的某种“平方根”。它们统称为“超对称(supersymmetries)”，能够提供能量特征子空间的新信息。本章讨论几个最简单的例子，即超对称量子力学系统。
§33 · en · machine_draft · machine-draft-not-reviewed
33 Supersymmetry, Some Simple Examples
If one considers fermionic and bosonic quantum systems that each separately have operators coming from Lie algebra or superalgebra representations on their state spaces, when one combines the systems by taking the tensor product, these operators will continue to act on the combined system. In certain special cases new operators with remarkable properties will appear that mix the fermionic and bosonic systems and commute with the Hamiltonian (these operators are often given by some sort of “square root” of the Hamiltonian). These are generically known as “supersymmetries” and provide new information about energy eigenspaces. In this chapter we’ll examine in detail some of the simplest such quantum systems, examples of “supersymmetric quantum mechanics”.