| Summary: | 碩士 === 國立臺灣大學 === 物理學研究所 === 106 === 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.
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