论文标题
非铁官汉密尔顿的双疗法状态路径积分量化
Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian
论文作者
论文摘要
我们首次介绍双疗法态路径集成，作为量化非炎症系统的方法。双晶态路径积分是作为普通相干状态路径积分的自然概括而产生的，这是赫尔米尔量子物理学所熟悉的。我们通过制定一个具体的示例来完成所有这些，即，计算Swanson模型的某个准 - 热变体的繁殖器，该模型在常规$ PT $转换下并不不变。由此产生的繁殖器与标准谐波振荡器的繁殖物的传播器相吻合，这是与相似性的相似性转化所考虑的模型相关的模型。我们还通过Feynman路径集成在位置空间中计算该模型的传播器，并验证两个结果的一致性。
We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from hermitian quantum physics. We do all this by working out a concrete example, namely, computation of the propagator of a certain quasi-hermitian variant of Swanson's model, which is not invariant under conventional $PT$-transformation. The resulting propagator coincides with that of the propagator of the standard harmonic oscillator, which is isospectral with the model under consideration by virtue of a similarity transformation relating the corresponding hamiltonians. We also compute the propagator of this model in position space by means of Feynman path integration and verify the consistency of the two results.
