论文标题
单模型hartle-hawking波数据包及其概率解释
Unimodular Hartle-Hawking wave packets and their probability interpretation
论文作者
论文摘要
我们从量子理论的角度重新检查了hartle-hawking波函数，该量子理论的角度从连接表示开始，并允许$λ$（如单模型理论），具有伴随的双重关系时间变量。通过将其结构转换为度量表示，我们发现了可正常化的hartle-Hawking波的非平凡的内部产品渲染波数据包，并且时间演化统一；但是，暗示的概率度量与幼稚的$ |ψ|^2 $有显着不同。与（单色）hartle-Hawking波函数相反，这些数据包形成了带有概率峰的行进波，除了在弹跳附近，事件和反射波介入，暂时重新形成常规的常驻波。远离反弹，数据包在公制空间和连接空间方面都变得更加清晰，这显然与海森伯格的原则矛盾，即即使该公制不是Hermitian，即使其特征值是真实的。在弹跳附近，逃生的波不仅渗透到经典的禁区，而且还延伸到$ a^2 <0 $ euclidean域。我们为该理论探讨了传播器，并将其与标准的传播者联系起来。 $ a = 0 $ point（又称“ nothing nothens”）是不明显的，在任何情况下，其中的波函数通常是不符合的和/或暗示$λ$的概率（宇宙将永远保存）。在该理论中，采用$λ$的适当函数的高斯状态更有意义，并使用与弹跳时间附近存在的逃生波相关的概率，以衡量产生一对时间对称性半经典的宇宙的可能性。
We re-examine the Hartle-Hawking wave function from the point of view of a quantum theory which starts from the connection representation and allows for off-shell non-constancy of $Λ$ (as in unimodular theory), with a concomitant dual relational time variable. By translating its structures to the metric representation we find a non-trivial inner product rendering wave packets of Hartle-Hawking waves normalizable and the time evolution unitary; however, the implied probability measure differs significantly from the naive $|ψ|^2$. In contrast with the (monochromatic) Hartle-Hawking wave function, these packets form travelling waves with a probability peak describing de Sitter space, except near the bounce, where the incident and reflected waves interfere, transiently recreating the usual standing wave. Away from the bounce the packets get sharper both in metric and connection space, an apparent contradiction with Heisenberg's principle allowed by the fact that the metric is not Hermitian, even though its eigenvalues are real. Near the bounce, the evanescent wave not only penetrates into the classically forbidden region but also extends into the $a^2<0$ Euclidean domain. We work out the propagators for this theory and relate them to the standard ones. The $a=0$ point (aka the "nothing") is unremarkable, and in any case a wave function peaked therein is typically non-normalizable and/or implies a nonsensical probability for $Λ$ (which the Universe would preserve forever). Within this theory it makes more sense to adopt a Gaussian state in an appropriate function of $Λ$, and use the probability associated with the evanescent wave present near the time of the bounce as a measure of the likelihood of creation of a pair of time-symmetric semiclassical Universes.
