AI 中文总结
本文对比惠勒-德维特方法与扩展相空间方法，指出正则量子化与考虑所有时空拓扑观点有矛盾，路径积分推导惠勒-德维特方程的渐近态假设存问题，扩展相空间方法基于路径积分，能导出薛定谔方程，有独特特点。
AI 中文摘要
本文旨在比较广义上理解的惠勒-德维特方法与一种替代方法，即所谓的引力量子化扩展相空间方法。这里的惠勒-德维特方法不仅指德维特1967年开创性论文中提出的量子几何动力学，还包括基于某种形式的惠勒-德维特方程的任何引力量子化方法。研究表明，正则量子化与量子引力创始人提出的应考虑所有可能时空拓扑的观点存在矛盾，路径积分方法似乎更合适，但从路径积分推导惠勒-德维特方程时关于渐近态的假设也存在问题。扩展相空间形式完全基于路径积分方法，拒绝渐近态假设会导致路径积分规范不变性无法证明，惠勒-德维特方程失去意义，而此替代方法能导出薛定谔方程，其特点值得探索。
英文摘要
The goal of this paper is to compare the Wheeler-DeWitt approach, understood in a broad sense, with an alternative one, the so-called extended phase space approach to quantization of gravity. By "the Wheeler-DeWitt approach", I mean not only quantum geometrodynamics formulated by DeWitt in his seminal paper of 1967, but also any approach to quantization of gravity based on the Wheeler-DeWitt equation in some form. Since the Wheeler-DeWitt equation is a direct consequence of the Dirac formalism, its analysis requires examination of the latter and its application to gravity. In particular, I argue that there is a contradiction between canonical quantization and the idea put forward by founders of quantum gravity that, in this theory, all possible spacetime topologies should be taken into account. The path integral approach seems to be more adequate then the canonical approach. However, to derive the Wheeler-DeWitt equation from the path integral, most authors make the assumption about asymptotic states, that again contradicts the supposition of arbitrary spacetime topology. The extended phase space formalism is entirely based on the path integral approach. Note that if one refuses the assumption about asymptotic states, one cannot prove the gauge invariance of the path integral, and the Wheeler-DeWitt equation loses its sense. In the alternative approach, one derives the Schrodinger equation instead. Thus, the extended phase space approach is really beyond the Wheeler-DeWitt approach. The features of this alternative approach are explored with special emphasis on conclusions that cannot be obtained by using the Wheeler-DeWitt quantum geometrodynamics.
Comments15 pages, no figure, to be published in Int. J. Mod. Phys. D
