标题： 洛伦兹破坏：QED中的环效应和观测约束 显示英文标题

标题： Lorentz Violation: Loop-Induced Effects in QED and Observational Constraints

摘要： 洛伦兹不变性是现代物理的基石，但其可能的破坏在理论上引人入胜，实验上也具有重要意义。 在本工作中，以量子电动力学为例，我们探讨了如何 将洛伦兹不变性破坏引入理论的特定部分，通过环状修正传播，修改其他粒子的传播和色散关系。 自能和真空极化图揭示了LIV效应如何跨部分传递，影响粒子运动学。 由于这些环效应，宇宙射线观测和其他 地球上的实验对产生的LIV参数施加了限制，否则这些参数将不受约束。 我们表明，虽然基于相互作用的LIV效应需要不现实大的参数才能被探测到，但对色散关系的修改可以在大型强子对撞机上探测到 $\delta \sim 10^{-8} \text{ to } 10^{-9}$ 。 这表明，基于加速器的共振研究为严格的LIV约束提供了一条有希望的途径，可能与天体物理观测相媲美。 显示英文摘要

摘要： Lorentz invariance is a cornerstone of modern physics, yet its possible violation remains both theoretically intriguing and experimentally significant. In this work, using quantum electrodynamics as an example, we explore how Lorentz invariance violation, introduced into a specific sector of the theory, spreads through loop corrections, modifying the propagation and dispersion relations of other particles. Self-energy and vacuum polarization graphs reveal how LIV effects transfer across sectors, influencing particle kinematics. Due to these loop effects, constraints from cosmic-ray observations and other Earth-based experiments impose limits on induced LIV parameters that would otherwise be less constrained. We show that while interaction-based LIV effects require unrealistically large parameters for detection, modifications to dispersion relations can be probed down to $\delta \sim 10^{-8} \text{ to } 10^{-9}$ at the LHC. This suggests that accelerator-based resonance studies provide a promising avenue for stringent LIV constraints, potentially rivaling astrophysical observations.