用拟正规模表示的开口腔的精确可解路径积分
Exactly solvable path integral for open cavities in terms of quasinormal modes
摘要：
我们计算了有漏腔中标量场的生成泛函的有限温度欧几里德相空间路径积分。如果源被限制在腔中，首先可以将外部的场积分，以获得仅对腔的有效作用。随后，人们使用的腔场在其准正规模式（QNM）的扩展-精确的，指数阻尼的经典演化算子，这以前已被证明是完整的一个大类的模型的本征态。耗散导致有效腔作用在QNM基中是非对角的。因此，求取高斯路径积分中固有的作用矩阵的逆以获得生成泛函是不平凡的，但可以通过调用新的QNM求和规则来完成。所得结果与以前用正则量子化得到的结果一致。
英文摘要：
We evaluate the finite-temperature Euclidean phase-space path integral for the generating functional of a scalar field inside a leaky cavity. Provided the source is confined to the cavity, one can first of all integrate out the fields on the outside to obtain an effective action for the cavity alone. Subsequently, one uses an expansion of the cavity field in terms of its quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the classical evolution operator, which previously have been shown to be complete for a large class of models. Dissipation causes the effective cavity action to be nondiagonal in the QNM basis. The inversion of this action matrix inherent in the Gaussian path integral to obtain the generating functional is therefore nontrivial, but can be accomplished by invoking a novel QNM sum rule. The results are consistent with those obtained previously using canonical quantization.
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