The local group velocity defined as the weak value of the velocity operator in (1 + 1)-dimensional Klein-Gordon and Dirac theory is studied. As shown by Berry [J. Phys. A 45, 185308 (2012)], when the pre- and post-selected states for evaluating the weak value are chosen at random from an ensemble of available states, it gives rise to a universal probability distribution for the local group velocity which can have both subluminal and superluminal components. In this work, we explore the possibility of enhancement of the superluminal fraction of this total probability distribution by applying a Lorentz boost and show that it can indeed be enhanced both in the case of Klein–Gordon and Dirac theories.

中文翻译：

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洛伦兹助推下超光速弱值的增强

研究了定义为(1+1)维Klein-Gordon和Dirac理论中速度算子的弱值的局部群速度。正如 Berry [J. 物理。A 45, 185308 (2012)]，当从可用状态集合中随机选择用于评估弱值的预选和后选状态时，它会产生局部群速度的通用概率分布，它可以具有包括超光速和超光速成分。在这项工作中，我们探索了通过应用 Lorentz boost 来增强该总概率分布的超光速部分的可能性，并表明它确实可以在 Klein-Gordon 和 Dirac 理论的情况下得到增强。