跡反常的古典有效理論和其在半古典量子重力的應用

Classical effective theory of trace anomaly and its application to semi-classical quantum gravity

沈哲民(Che-Min Shen)

指導教授 ： 陳丕燊

共同指導教授 ： 泉圭介(Keisuke Izumi)

國立臺灣大學/理學院/物理學研究所/博士(2016年)

https://doi.org/10.6342/NTU201603464

摘要

我們在這篇論文中探討過去一直被忽略的二維與四維時空中跡反常作用量的邊界效應. 在引進了輔助純量場後化簡得到的局部跡反常作用量可以被利用來推導能量動量張量的量子期望值. 雖然輔助純量場的解中的自由度可以對應來描述物質場的不同量子態早已廣為人知, 但此兩者間的對應關係如何清楚的理解至今仍不甚清楚. 我們證明了在考慮了跡反常作用量的邊界效應後, 這個過去不清楚的對應關係被找到了. 從此，此考慮了邊界效應的跡反常作用量將可作為一成熟獨立的工具，用做為計算彎曲時空量子場論中重整化能量動量張量的一種選擇。同時, 我們也因此發現了跡反常作用量的額外使用限制條件, 那就是跡反常作用量只能被應用在歐拉特徵數為零的時空. 雖然在二維有邊界的時空歐拉特徵數總是為零, 但是在四維時空中卻不保證永遠成立. 最後, 我們把考慮了邊界效應的跡反常作用量應用在幾種常見的時空跟量子重力問題以供做應用的參考例子. 藉此展示把這套方法用來計算彎曲時空的量子效應時是如何的強效. 我們預期這套新方法可以成為一種相當有用的工具, 來研究某些有趣的量子重力問題.
這篇論文是建立[1, 2] 這兩篇工作上。其中[1] 已經被發表，而[2]
也將在近期投稿發表。

關鍵字

量子重力 ； 彎曲空間裡的量子場論 ； 黑洞的量子效應, 霍金輻射, 黑洞熱力學.

並列摘要

We discuss the boundary effect of anomaly-induced action in 2-dimensional and 4-dimensional spacetime, which is ignored in previous studies. Anomalyinduced action, which gives the stress tensor with the same trace as the trace
anomaly, can be represented in terms of local operators by introducing an auxiliary scalar field. Although the degrees of freedom of the auxiliary field can in principle describe the quantum states of the original field, the correspondence between them was unclear. We show that, by considering the boundary effect, the missing correspondence will be restored. Therefore, from now on, this technique has become a mature and independent tool to calculate the renormalized stress tensor in curved spacetime. Also, we find that the anomaly-induced action can only be used for the spacetime with zero Euler characteristic which is in general not true in 4-dimension. As examples, we demonstrate our formalism via several different spacetime and famous quantum gravity issues to show how efficient and powerful this approach is. We expect that our new formalism can become an useful tool to study various interesting quantum gravity effects.
This thesis is based on the works [1, 2]. [1] is already published and [2] is about to be submitted for publication.

並列關鍵字

Quantum gravity ； Quantum fields in curved spacetime ； Quantum aspects of black holes, evaporation, thermodynamics.

參考文獻

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