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.

中文翻译：

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非厄米哈密顿量的双相干态路径积分量化

我们首次引入双相干状态路径积分作为量化非厄米系统的方法。双相干态路径积分作为普通相干态路径积分的自然推广而出现，这在厄密量子物理学中很常见。我们通过一个具体的例子来完成这一切，即计算斯旺森模型的某个准厄米变体的传播子，它在传统的 $PT$ 变换下不是不变的。得到的传播子与标准谐振子的传播子的传播子一致，由于与相应的哈密顿量相关的相似变换，标准谐振子的传播子与所考虑的模型等谱。