论文标题
扩展不确定性原理通过DIRAC量化
Extended Uncertainty Principle via Dirac Quantization
论文作者
论文摘要
统一的量子理论和重力仍然是物理学的基本挑战。尽管大多数现有文献都集中于由于重力引起的量子理论的紫外线（UV）修改，但这项工作表明，当我们在弯曲时空中描述量子理论时，会出现通用红外（IR）修改。我们明确地证明了对位置摩肌代数的修改与曲率不变性成正比（例如RICCI标量和Kretschmann鳞片）。我们的结果是通过严格应用狄拉克的量化程序得出的，表明量子系统中的红外效应可以公理地得出。我们通过将它们嵌入更高维平的几何形状中，研究任意弯曲的时空中的粒子动力学。我们的方法涉及将粒子动力学嵌入高维平坦的几何形状并利用Dirac的量化过程中，使我们能够通过修改的位置 - 摩托明代数来捕获粒子在4维弯曲的时空中的动力学。当应用于各个空间时，该方法表明，由于时空曲率的校正是通用的。我们将我们的结果与使用扩展的不确定性原理得出的结果进行比较。最后，我们讨论了我们工作对黑洞和纠缠的含义。
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR) modifications arise when we describe quantum theory in curved spacetime. We explicitly demonstrate that the modifications to the position-momentum algebra are proportional to curvature invariants (such as the Ricci scalar and Kretschmann scalar). Our results, derived through a rigorous application of Dirac's quantization procedure, demonstrate that infrared effects in quantum systems can be axiomatically derived. We study particle dynamics in an arbitrary curved spacetime by embedding them in a higher-dimensional flat geometry. Our approach, which involves embedding particle dynamics in a higher-dimensional flat geometry and utilizing Dirac's quantization procedure, allows us to capture the dynamics of a particle in 4-dimensional curved spacetime through a modified position-momentum algebra. When applied to various spacetimes, this method reveals that the corrections due to the spacetime curvature are universal. We further compare our results with those derived using extended uncertainty principles. Finally, we discuss the implications of our work for black holes and entanglement.
