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arXiv 2108.07023gr-qcquant-ph
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具有最优控制路径积分的圈量子引力及其在黑洞隧穿中的应用

Loop quantum gravity with optimal control path integral, and application to black hole tunneling

Quentin Ansel

摘要:

本文从最优控制理论的观点出发,提出了爱因斯坦引力理论的一种新的路径积分形式。尽管最优控制与物理学家们熟知的变分原理有着密切的关系,但它却被证明是更一般的。在这种情况下,拉格朗日不同于爱因斯坦-希尔伯特拉格朗日的定义。利用新的作用量泛函,精确地恢复了爱因斯坦场方程.量子理论是用Ashtekar变量和圈标积得到的。通过例子,用一个玩具模型研究了一个黑洞隧穿到另一个黑洞或一个白洞的过程。

英文摘要:

This paper presents a novel path integral formalism for Einstein's theory of gravitation from the viewpoint of optimal control theory. Despite its close relation to the well-known variational principles of physicists, optimal control turns out to be more general. Within this context, a Lagrangian different from the Einstein-Hilbert Lagrangian is defined. Einstein field equations are recovered exactly with variations of the new action functional. The quantum theory is obtained using Ashtekar variables and the loop scalar product. By means of example, the tunneling process of a black hole into another black hole or into a white hole is investigated with a toy model.

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