可积Toda系统作为Mixmaster各向异性的量子近似
Integrable Toda system as a quantum approximation to the anisotropy of Mixmaster
摘要：
我们提出了一种研究Mixmaster宇宙量子动力学的正则化方法，该方法允许用显式可积周期性3粒子Toda系统来近似各向异性势。这种方法是基于协变Weyl-Heisenberg积分量子化。这样一个过程自然放大了底层户田系统的动力学作用，通过平滑的三个峡谷的各向异性潜力。由于相应的本征函数可以明确地构造，我们的发现铺平了道路，一种新的微扰方法的量子Mixmaster动力学。
英文摘要：
We present a regularisation approach to the study of the quantum dynamics of the Mixmaster universe which allows to approximate the anisotropy potential with the explicitly integrable periodic 3-particle Toda system. This approach is based on a covariant Weyl-Heisenberg integral quantization. Such a procedure naturally amplifies the dynamical role of the underlying Toda system by smoothing out the three canyons of the anisotropy potential. Since the respective eigenfunctions can be explicitly constructed, our finding paves the way to a novel perturbative approach to the quantum Mixmaster dynamics.
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