arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1111.2192gr-qc
收藏

对量子引力问题的一点看法

A view on the problems of Quantum Gravity

T. P. Shestakova

摘要:

现有的引力量子化方法都是按照Wheeler-DeWitt几何动力学的思想给出三维几何的量子描述。在这种描述中,规范引力自由度的作用被忽略了。一个可能的替代方案是考虑扩展相空间中的引力动力学,同时考虑到广义相对论和其他场论之间的区别。扩展相空间中的表述导致了经典和量子水平上的一些结果。在经典层次上,它保证了哈密顿动力学与拉格朗日动力学完全等价,保证了Poisson括号代数在包括规范变量的重参数化在内的足够广泛的重参数化下是不变的,同时在正则狄拉克方法中约束代数不是不变的,这就产生了量子化的问题。在量子层次上,这种方法达到了这样的描述,即观察者可以在不同的参考系中看到各种各样但互补的量子引力现象,这回答了广义相对论和量子理论的精神。虽然到目前为止,这种方法被应用于广义相对论的原始公式,但它在不同趋势中的实现,包括量子环引力或其他一些引力变量的表示,也会引起人们的兴趣。

英文摘要:

The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is missed. A probable alternative is to consider gravitational dynamics in extended phase space, taking into account the distinctions between General Relativity and other field theories. The formulation in extended phase space leads to some consequences at classical and quantum levels. At the classical level, it ensures that Hamiltonian dynamics is fully equivalent to Lagrangian dynamics, and the algebra of Poisson brackets is invariant under reparametrizations in a wide enough class including reparametrizations of gauge variables, meantime in the canonical Dirac approach the constraints' algebra is not invariant that creates problems with quantization. At the quantum level, the approach come to the description in which the observer can see various but complementary quantum gravitational phenomena in different reference frames that answers the spirit of General Relativity and Quantum Theory. Though until now the approach was applied to General Relativity in its original formulations, its implementation in different trends, including Quantum Loop Gravity or some other representations of gravitational variables, would also be of interest.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑