Violation of the null energy condition plays an important role both in the general theory of relativity and quantum field theory in curved spacetimes. Over the years, it has been shown that the violation of the null energy condition leads to instability and violation of causality. In quantum field theory, violation of the energy condition also depends on the quantum states apart from the geometry of curved spacetime. Hence, the quantum effects play an important role in the violation of the null energy condition. We show that the set of all the coherent states does not violate the null energy condition. Further, we also show that under certain conditions, the null energy condition is violated either by a pure state or a mixed state. Furthermore, the dynamical violation of the null energy condition by the quantum states is also discussed here.

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基于零能量条件的量子态分类

违反零能量条件在广义相对论和弯曲时空中的量子场论中都起着重要作用。多年来，已经表明违反零能量条件会导致不稳定和违反因果关系。在量子场论中，能量条件的违反也取决于弯曲时空几何之外的量子态。因此，量子效应在违反零能量条件方面起着重要作用。我们证明了所有相干状态的集合不违反零能量条件。此外，我们还表明，在某些条件下，纯态或混合态都违反了零能量条件。此外，这里还讨论了量子态对零能量条件的动态破坏。