自發對稱破缺在散射幅度之體現

The Manifestation of Spontaneous Symmetry Breaking on Scattering Amplitudes

張順晴(Shun-Qing Zhang)

指導教授 ： 黃宇廷

國立臺灣大學/理學院/物理學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201704348

摘要

Soft-定理揭示了無質量粒子相互作用的理論的基本對稱性。本文首先利用流代數之非微擾之方式導出單一Soft-定理。那麼我們期望雙重soft-定理，就如同單一soft-定理一樣，是從對稱性原理出發的。然而，最近將這種流代數的方法推廣到已知雙重soft-定理的嘗試遇到了困難。在這項工作中，我們已經將難度追溯到兩個不等價的soft 動量展開，這取決於soft 限制是不對稱的還是對稱的，我們分別表示為A 型（順序soft）和B 型（同時soft）。類型A 的soft行為可以直接從連續兩次作用單一soft-定理導出，因此是非微擾保護的。對於類型B，需要加入四點的信息來確定相應的soft-定理，因此通常不受保護。 我們還要問，是否可以從局域性以及兩種soft-定理導出幺正性。 最後，我們研究規模和共形不變性之間的相互作用。

關鍵字

散射振幅 ； 自發對稱破缺 ； soft-定理 ； ?正性 ； 共形對稱

並列摘要

Soft theorems reveal the underlying symmetry of the theory and constrain the interaction of massless particles. In this thesis, we first derive single soft theorems in a non-perturbative fashion by employing current algebras. Then we expect double-soft theorems, like its single-soft counterparts, to arise from the underlying symmetry principles. However, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A(sequentially soft) and type B(simultaneously soft) respectively. The soft-behavior for type A scheme can be directly derived from single soft theorems, and are thus non-perturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems. Finally, we study the interplay between scale and conformal invariance in this context.

並列關鍵字

Scattering Amplitudes ； Spontaneous Symmetry Breaking ； Soft Theorem ； Unitarity ； Conformal Symmetry

參考文獻

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