非线性响应理论中的规范不变性和沃德恒等式
Gauge invariance and Ward identities in nonlinear response theory
摘要：
我们提出了一个正式的分析非线性响应函数的关联函数在实时和非实时域。特别是，我们表明，因果关系的非线性响应函数，表示在实时嵌套的迭代器，可以从时间顺序的响应函数，这是更容易服从图解计算的解析延续。这推广了线性响应理论的著名结果。然后，我们使用规范不变性参数导出密度和电流通道的二阶响应函数之间的精确关系。这些身份，这是非微扰的粒子间相互作用的强度，使我们能够建立在不同的电磁计完成的非线性光学计算之间的精确连接。
英文摘要：
We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.
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