雙重弱動量定理的對稱性基礎

與單一弱動量定理相同，雙重弱動量定理源自於規範無質量粒子交互作用的對稱性原理。雖然使用流代數可以非微擾地導出單一弱動量定理，將此方法拓展到已知的雙重弱動量定理的嘗試在近期屢遭困難。在本文中，我們指出這些困難來自於雙重弱動量極限的兩種定義：A 類是將兩個粒子各自取弱動量極限，B 類則是兩個粒子以相同參數趨近於零。推導 A 類極限只需要單一弱動量定理，而 B 類極限尚需四點交互作用的資訊，因此只有 A 類極限完全相容於量子修正。同時，本文的分類方式也能輕易地推廣到多重弱動量定理。另外，我們也探討了一個未被完全研究的課題：能否從這兩類定理與局部性原理得到么正性原理。

關鍵字

等效場論；散射幅度；自發對稱性破缺

並列摘要

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, 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 and B respectively. The soft-behaviour for type A scheme can simply be 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. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.

並列關鍵字

Effective Field Theories ； Scattering Amplitudes ； Spontaneous Symmetry Breaking

參考文獻

[1] S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.

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