标量场量子宇宙学：薛定谔图像
Scalar field quantum cosmology: a Schrödinger picture
摘要：
本文研究了标量场Friedmann-Robertson-Walker（FRW）宇宙学的经典模型和量子模型，并着眼于量子宇宙学中的时间问题。我们在作用量的标量场扇区上引入一个正则变换，使得与新正则变量共轭的动量在变换后的哈密顿量中线性出现。使用这个正则变换，我们表明，它可能导致识别相应的动力系统的时间参数。在平坦、封闭和开放的FRW宇宙的情况下，通过引入时间参数得到了经典宇宙学解。此外，这种形式主义产生了薛定谔-惠勒-德维特方程，用于对所考虑的模型进行量子力学描述，其本征函数可以用来构造宇宙的波函数。我们利用所得到的波函数，通过量子宇宙学的多世界和本体论解释，研究了由于量子效应对经典宇宙学的可能修正。
英文摘要：
We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.
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