Constructing scattering amplitudes from their formal properties
Abstract/Contents
- Abstract
- Scattering amplitudes in quantum field theory encode the probability of configurations of incoming and outgoing particles scattering into each other, as well as particle masses and decay rates. Traditionally they have been calculated using Feynman diagrams, but this method generally proves too computationally intensive to allow for the calculation of higher-loop contributions, which are relevant for making predictions in particle physics experiments and to our understanding of quantum field theory itself. As a step in the direction of filling this computational gap, this dissertation presents an improved bootstrap method for computing scattering amplitudes in the planar limit of maximally supersymmetric Yang-Mills theory. This method does away with Feynman diagrams altogether, and instead uses knowledge of the symmetries and analytic properties of scattering amplitudes, in conjunction with an understanding of the mathematical form these amplitudes take in general and special kinematics, to uniquely determine them at high loop orders. In particular, it makes use of the fact that amplitudes in this theory are expressible in terms of generalized polylogarithms for seven and fewer particles. The first part of this dissertation focuses on six-particle kinematics, where previously-unappreciated algebraic constraints on these amplitudes are described that restrict both their double derivatives and their double discontinuities. Alongside previously-understood constraints, these properties are used to uniquely determine all six-particle amplitudes in this theory through five loops. These explicit results are then used to provide analytic and numerical evidence for a recently-conjectured positivity property these amplitudes are thought to have in certain kinematic regions. In the second part of this dissertation, it is shown that these methods straightforwardly generalize to seven-particle kinematics, where they in fact prove to be even more restrictive than in six-particle kinematics. In particular, a smaller set of constraints is shown to be sufficient to determine specific seven-point amplitudes at three and four loops, up to integration constants. While the results presented in this thesis are confined to the planar limit of maximally supersymmetric Yang-Mills theory, these bootstrap methods are expected to prove useful even in theories without supersymmetry.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | McLeod, Andrew |
|---|---|
| Associated with | Stanford University, Department of Physics. |
| Primary advisor | Dixon, Lance |
| Thesis advisor | Dixon, Lance |
| Thesis advisor | Graham, Peter (Peter Wickelgren) |
| Thesis advisor | Kallosh, Renata |
| Advisor | Graham, Peter (Peter Wickelgren) |
| Advisor | Kallosh, Renata |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Andrew McLeod. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Andrew J. McLeod
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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