论文标题
渐近概括扩展不确定性原理
Asymptotic Generalized Extended Uncertainty Principle
论文作者
论文摘要
我们提出了一种形式主义，该形式允许对任意空间曲率模型和观察者的扩展不确定性原理（EUP）的扰动推导。进入小位置不确定性领域，我们得出了一般的渐近EUP。领先的第二阶曲率诱导的校正与RICCI标量成正比，而第四阶校正具有0级CARTAN不变的PSI^2（曲率张量中的标量二次）和RICCI的弯曲空间拉普拉克良好的RICCI标准级，其所有这些均处于衡量位置运算仪的期望值，即在衡量位置运算符时，即在衡量位置经验执行仪的衡量。首先对此结果进行了验证，以用于先前衍生的均质空间模型，然后应用于其他非平整曲率相关效果，例如不均匀性，旋转和各向异性应力流体，从而导致黑洞“头发”。 我们的主要成就结合了我们介绍的方法与普遍的不确定性原理（GUP）结合了变形的换向因子，以制定我们称为渐近概括的扩展不确定性原理（年龄）的通用形式。
We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant Psi^2 (a scalar quadratic in curvature tensors) and the curved space Laplacian of the Ricci scalar all of which are evaluated at the expectation value of the position operator, i.e. the expected position when performing a measurement. This result is first verified for previously derived homogeneous space models and then applied to other non-trivial curvature related effects such as inhomogeneities, rotation and an anisotropic stress fluid leading to black hole "hair". Our main achievement combines the method we introduce with the Generalized Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a generic form of what we call the Asymptotic Generalized Extended Uncertainty Principle (AGEUP).
