非反交换理论的隐厄米性
Crypto-Hermiticity of nonanticommutative theories
摘要：
我们注意到，虽然闵可夫斯基超对称理论的非反对易变形不遵守现实条件，并似乎导致非厄米哈密顿量H，后者属于一类隐厄米（或准厄米）哈密顿量最近吸引了相当大的关注。它们可以通过相似变换H -> e^R H e^{-R}与适当选择的R而明显地成为厄米特的。变形模型与未变形模型具有相同的超对称性代数，但在某些情况下很难写出一半超荷的显式表达式。变形的SQM模型完全有意义。目前还不清楚这是否也是NAC闵可夫斯基场论的情况--传统定义的S-矩阵在那里不是酉的。
英文摘要：
We note that, though nonanticommutative deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of crypto-Hermitian (or quasi-Hermitian) Hamiltonians having attracted recently a considerable attention. They can be made manifestly Hermitian via the similarity transformation H -> e^R H e^{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one though it is difficult in some cases to write explicit expressions for a half of supercharges. The deformed SQM models make perfect sense. It is not clear whether it is also the case for NAC Minkowski field theories -- the conventionally defined S--matrix is not unitary there.
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