[论文解读] Effects of Non-locality in Gravity and Quantum Theory

Jens Boos|arXiv (Cornell University)|Jan 1, 2020

Cosmology and Gravitation Theories参考文献 258被引用 6

一句话总结

本文研究了引力与量子力学中的洛伦兹不变、无鬼魅的非局域理论，引入长度参数 ℓ 以量化非局域性。研究表明，非局域性可调节引力奇点，改变量子系统的散射行为，并影响真空涨落，同时保持宏观因果性与霍金辐射通量不变，且黑洞熵对非局域效应敏感。

ABSTRACT

Spacetime—the union of space and time—is both the actor and the stage during physical processes in our fascinating Universe. In Lorentz invariant local theories, the existence of a maximum signalling speed (the “speed of light”) determines a notion of causality in spacetime, distinguishing the past from the future, and the cause from the effect. This thesis is dedicated to the study of deviations from locality. Focussing on a particular class of non-local theories that is both Lorentz invariant and free of ghosts, we aim to understand the effects of such non-local physics in both gravity and quantum theory. Non-local ghost-free theories are accompanied by a parameter ℓ of dimension length that parametrizes the scale of non-locality, and for that reason we strive to express all effects of non-locality in terms of this symbol. In the limiting case of ℓ = 0 one recovers the local theory, and the effects of non-locality vanish. In order to address these questions we develop the notion of non-local Green functions, study their causal properties, and demonstrate that non-locality leads to a violation of causality on small scales but may be recovered at macroscopic distances much larger than the scale of non-locality. In particular, we utilize non-local Green functions to construct the stationary gravitational field of point particles and extended bodies in the weak-field limit of non-local gravity and demonstrate explicitly that non-locality regularizes gravitational singularities at the linear level. Boosting these solutions to the speed of light in a suitable limit, we obtain a class of geometries corresponding to non-local regular ultrarelativistic objects. In the context of quantum mechanics we demonstrate that non-locality affects the scattering coefficients of a scalar field in the presence of a δ-shaped potential: for a critical frequency, the potential becomes completely opaque and reflects 100% of the incoming wave of that frequency. In the realm of non-local quantum field theory we first illustrate that non-locality smoothes the vacuum polarization and thermal fluctuations in the vicinity of a δ-shaped potential and then prove the fluctuation-dissipation theorem in this particular case. Turning towards quantum field theory in curved spacetime, we construct a non-local ghost-free generalization of the Polyakov effective action and evaluate the resulting quantum average of the energy-momentum tensor in the background of a two-dimensional black hole. While non-locality does not affect the asymptotic flux of Hawking radiation in this model, the entropy of the black hole is sensitive to the presence of non-locality. The results presented in this thesis establish several effects of a Lorentz invariant, ghost-free non-locality in the areas of both gravitational and quantum physics.

研究动机与目标

• 研究洛伦兹不变、无鬼魅非局域性在引力与量子系统中的物理后果。
• 理解以长度参数 ℓ 参数化的非局域性如何影响因果性、奇点与散射过程。
• 构建非局域格林函数，并将其应用于弱场引力与弯曲时空中的量子场论。
• 研究非局域性对真空极化、热涨落与涨落-耗散定理的影响。
• 评估非局域推广的泡利夫有效作用量及其对黑洞熵与霍金辐射的影响。

提出的方法

• 开发非局域格林函数以分析非局域理论中的因果结构与传播特性。
• 采用弱场近似，推导点质量与扩展物体在非局域引力中的静态引力场。
• 应用非局域格林函数计算入射标量场在 δ 形势阱上的散射系数。
• 分析非局域量子场论中 near δ 势阱的真空极化与热涨落。
• 构建二维黑洞非局域鬼魅无害的泡利夫有效作用量推广。
• 评估非局域模型中能量-动量张量的量子平均值与霍金辐射通量。

实验结果

研究问题

• RQ1 以 ℓ 参数化的非局域性如何影响时空的因果结构与信号传播？
• RQ2 在引力线性化理论中，非局域性在多大程度上调节了引力奇点？
• RQ3 非局域性如何改变标量波在 δ 形势阱上的散射，特别是在临界频率下？
• RQ4 非局域性是否改变了势阱或边界附近的真空极化与热涨落？
• RQ5 在非局域泡利夫模型中，非局域性对二维黑洞的熵与霍金辐射有何影响？

主要发现

• 非局域性在小尺度上导致因果性破坏，但在远大于 ℓ 的距离上恢复宏观因果性。
• 非局域引力在线性层次上明确调节了引力奇点，消除了点质量处的发散。
• 在临界频率下，δ 形势阱因非局域效应而完全反射，表明波被完全抑制。
• 非局域性使 δ 势阱附近的真空极化与热涨落更加平滑，且在此背景下涨落-耗散定理依然成立。
• 非局域泡利夫有效作用量的推广得到的量子能量-动量张量对霍金辐射的渐近通量不敏感于非局域性。
• 非局域模型中黑洞熵依赖于非局域尺度 ℓ，表明热力学量对非局域结构具有直接敏感性。