沿稳态世界线的量子能量不等式
Quantum Energy Inequalities along stationary worldlines
AI总结：
本文在四维闵可夫斯基时空中研究无质量最小耦合标量场沿稳态世界线的量子能量不等式，用世界线曲率不变量给出下界的闭式表达式，并通过六种典型世界线验证，发现惯性及匀加速情形分别由闵可夫斯基真空和林德勒真空达到下界。
摘要：
量子能量不等式（QEIs）是量子场平均能量密度的下界。它们已在一般弯曲时空中的多种场论中得到证明，但显式下界通常难以以闭式形式计算。本文研究四维闵可夫斯基时空中无质量最小耦合标量场沿稳态世界线——即速度在单参数洛伦兹子群作用下演化的曲线——的量子能量不等式，并以世界线的曲率不变量给出量子能量不等式下界的闭式表达式。我们的一般结果通过对六种典型稳态世界线的具体计算加以说明。当平均周期趋于无穷时，量子能量不等式下界与世界线上的恒定能量密度相一致。对于惯性世界线和匀直线加速世界线，该常数值分别由闵可夫斯基真空和林德勒真空达到。对于其他稳态世界线的下界是否能由其他感兴趣的状态达到，仍是一个未解决的问题。
英文摘要：
Quantum energy inequalities (QEIs) are lower bounds on the averaged energy density of a quantum field. They have been proved for various field theories in general curved spacetimes but the explicit lower bound is not easily calculated in closed form. In this paper we study QEIs for the massless minimally coupled scalar field in four-dimensional Minkowski spacetime along stationary worldlines - curves whose velocity evolves under a 1-parameter Lorentz subgroup -- and find closed expressions for the QEI bound, in terms of curvature invariants of the worldline. Our general results are illustrated by specific computations for the six protoypical stationary worldlines. When the averaging period is taken to infinity, the QEI bound is consistent with a constant energy density along the worldline. For inertial and uniformly linearly accelerated worldlines, this constant value is attained by the Minkowski and Rindler vacuums respectively. It is an open question as to whether the bounds for other stationary worldlines are attained by other states of interest.
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