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arXiv 2001.00556gr-qchep-thmath-phmath.MP
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量子宇宙学中的经典宇宙

Classical Universe Arising from Quantum Cosmology

S. Jalalzadeh, M. Rashki, S. Abarghouei Nejad

摘要:

本文将形变量子化的Weyl-Wigner-Groenewold-Moyal形式应用于具有正空间曲率和共形耦合标量场的均匀各向同性宇宙的量子宇宙学,研究了量子宇宙学的经典极限和幺正演化.相应的量子宇宙学(类似于量子宇宙学的正则量子化方案中的薛定谔解释)由Moyal-Wheeler-DeWitt方程描述,该方程在Moyal相空间中有一个精确解,导致Wigner准概率分布函数,峰值超过经典解。我们表明,对于一个大的值的量子数$n$,出现的经典宇宙充满了辐射与量子力学的起源。同时,我们在模型的标量场扇区上引入正则变换,使得新正则变量的共轭动量线性地出现在变换后的总哈密顿量中。利用这种正则变换,我们表明,它可能会导致解开时间从真正的动力学变量。我们得到了相干态和压缩态的含时维格纳函数。我们表明,这些维格纳函数的峰值遵循相空间中的经典轨迹。

英文摘要:

In this paper, we study the classical limit and unitary evolution of quantum cosmology by applying the Weyl--Wigner--Groenewold--Moyal formalism of deformation quantization to quantum cosmology of a homogeneous and isotropic universe with positive spatial curvature and conformally coupled scalar field. The corresponding quantum cosmology (similar to the Schrödinger interpretation in canonical quantization scheme of quantum cosmology) is described by the Moyal--Wheeler--DeWitt equation which has an exact solution in Moyal phase space, resulting in Wigner quasiprobability distribution function, peaking over the classical solutions. We show that for a large value of the quantum number $n$, the emerged classical universe is filled with radiation with quantum mechanical origin. Also, we introduce a canonical transformation on the scalar field sector of the model such that the conjugate momenta of the new canonical variable appear linearly in the transformed total Hamiltonian. Using this canonical transformation, we show that, it may lead to disentangle the time from the true dynamical variables. We obtain the time-dependent Wigner function for a coherent as well as for squeezed states. We show that the peak of these Wigner functions follows the classical trajectory in the phase space.

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