量子化時空與黑洞的半古典穿隧

Abstract

第一部分我們建立了一個擁有自旋性質的時空量子化模型，這個模型的出發 點是建立在改良由陳丕燊教授在史丹佛大學的同事R.J. Adler提出對於時空代數的 調整。我們得出了一個在小尺度下不連續的時空模型，並且連結到迴圈量子重力 以及超弦理論。我們預測了廣義話的測不準原理、全像的性質以及在觀測上的預 測。這份工作是與蔣序文合作並在陳丕燊教授指導下完成，結果發表於Physical Review D。 第二部分我們研究了時空與黑洞的半古典穿隧，我們詳細的學習了薄殼瞬 子(thin-shell instanton)的性質以及其物理上的詮釋;我們給出了在文獻中提及的 兩種詮釋為等價的證明，並且藉此驗證在一定的條件下正則(canonical)與歐氏路 徑積分(Euclidean path integral)的處理方法會得到同樣的物理結果，可以幫助人 們對於歐氏路徑積分處理量子宇宙或量子重力有更深的了解。這份工作是與廉 東漢(Dong-han Yeom)博士合作並在陳丕燊教授指導下完成，結果發表於Physical Review D。 第三部分是我在瑞典斯德哥爾摩大學(Stockholm University)以及北歐五國理論 物理研究中心(NORDITA)訪問並在Ingemar Bengtsson教授指導下的研究結果，我 們主要目標是了解時空邊界的BMS群;我們詳細的學習了電磁場在時空邊界的性 質。

The first part of my thesis is about a spinorial quantization of spacetime. Motivated by both concepts of R.J. Adler’s recent work on utilizing Clifford algebra as the linear line element ds = γμ dXμ, and the fermionization of the cylindrical world-sheet Polyakov action, we introduce a new type of spacetime quantization that is fully covariant. The theory is based on the reinterpretation of Adler’s linear line element as ds = γμ λγμ , where λ is the characteristic length of the theory. We name this new operator as 'spacetime interval operator', and argue that it can be regarded as a natural extension to the one-forms in the U(su(2)) non-commutative geometry. By treating Fourier momentum as the particle momentum, the generalized uncertainty principle of the U(su(2)) non-commutative geometry, as an approximation to the generalized uncertainty principle of our theory, is derived, and is shown to have a lowest order correction term of the order p2 similar to that of Snyder’s. The holography nature of the theory is demonstrated, and the predicted fuzziness of the geodesic is shown to be much smaller than conceivable astrophysical bounds. The second part of my thesis is about semiclassical solution in black hole physics. For O(4)-symmetric instantons, there are two complementary interpretations for their analytic continuations. One is the nothing-to-something interpretation, where the initial and the final hypersurfaces are disconnected by Euclidean manifolds. The other is the something-to-something interpretation, introduced by Brown and Weinberg, where the initial and the final hypersurfaces are connected by the Euclidean manifold. These interpretations have their own pros and cons and hence these are complementary. In this paper, we consider analytic continuations of thin-shell instantons that have less symmetry, i.e., the spherical symmetry. When we consider the Farhi-Guth-Guven/Fischler-Morgan-Polchinski tunneling, the something- to-something interpretation has been used in the usual literature. On the other hand, we can apply the nothing-to-something interpretation with some limited conditions. We argue that even for both interpretations, we can give the consistent decay rate. As we apply and interpret following the nothing-to-something interpretation, a stationary black hole can emit an expanding shell that results a spacetime without a singularity nor an event horizon. The third part of my these is about asymptotic electromagnetic field behaviors on null infinities, which is based on my studies at Stockholm University and NORDITA in Sweden.