The anomalous generation of chirality with mass effects via the axial Ward identity and its dependence on the Schwinger mechanism is reviewed, utilizing parity violating homogeneous electromagnetic background fields. The role vacuum asymptotic states play on the interpretation of expectation values is examined. It is discussed that observables calculated with an in–out scattering matrix element predict a scenario under Euclidean equilibrium. A notable ramification of which is a vanishing of the chiral anomaly. In contrast, it is discussed observables calculated under an in–in, or real-time, formalism predict a scenario out-of equilibrium, and capture effects of mean produced particle–antiparticle pairs due to the Schwinger mechanism. The out-of equilibrium chiral anomaly is supplemented with exponential quadratic mass suppression as anticipated for the Schwinger mechanism. Similar behavior in and out-of equilibrium is reviewed for applications including the chiral magnetic effect and chiral condensate.

中文翻译：

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具有质量效应的手性产生——施温格对产生和轴向沃德身份

回顾了通过轴向沃德恒等式产生具有质量效应的手性异常产生及其对施温格机制的依赖性，利用违反均匀电磁背景场的宇称。研究了真空渐近状态在解释期望值中所起的作用。讨论了用进出散射矩阵元素计算的可观测量预测欧几里得平衡下的情景。其中一个显着的后果是手征异常的消失。相比之下，讨论了在实时或实时形式下计算的可观察量预测了一个不平衡的场景，并捕获了由于施温格机制而产生的平均粒子-反粒子对的影响。正如 Schwinger 机制所预期的那样，失衡的手性异常辅以指数二次质量抑制。对包括手性磁效应和手性凝聚物在内的应用的类似行为进行了审查。