论文标题
分解的希尔伯特空间指标和非交通式准热观测值
Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables
论文作者
论文摘要
众所周知，具有真实特征值的（一般，非共同）的非官员$λ_J$不一定代表可观察到的物品。我们描述了一种特定类别的量子模型，其中这些操作员加上基本的Hilbert-Space度量$θ$均以辅助操作员$ $（n+1）-$ plet $ z_k $，$ k = 0,1，\ ldots，n $表示。我们的形式主义退化为$ {\ cal pt} - $ $ n = 2 $的对称量子力学，带公制$θ= z_2z_1 $，parity $ {\ cal p} = z_2 $，电荷$ {\ cal c}
It is well known that an (in general, non-commutative) set of non-Hermitian operators $Λ_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus the underlying physical Hilbert-space metric $Θ$ are all represented in terms of an auxiliary operator $(N+1)-$plet $Z_k$, $k=0,1,\ldots,N$. Our formalism degenerates to the ${\cal PT}-$symmetric quantum mechanics at $N=2$, with metric $Θ=Z_2Z_1$, parity ${\cal P}=Z_2$, charge ${\cal C}=Z_1$ and Hamiltonian $H=Z_0$.
