- Title Information
- Title
- Landau Singularities and Positive Geometries
- Name:
Personal
- Name Part
- Stanojevic, Stefan
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Spradlin, Marcus
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Jevicki, Antal
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Alexander, Stephon
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Physics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2020
- Physical Description
- Extent
- 9, 109 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2020
- Genre (aat)
- theses
- Abstract
- This work studies the analytical structure of scattering amplitudes in a class of toy models,
from the perspective of novel geometrical structures underlying scattering amplitudes, and
utilizing discrete mathematics. We find the set of all-loop n - point Landau singularities of the
first type arising in any massless planar theory using graph operations inspired by the theory of electrical circuits.
We also describe how to find the set of possible branch points of amplitudes at any fixed loop
order and all particle multiplicities in planar N = 4 SYM theory, using the information contained
in the boundaries of the amplituhedra. Along the way, we devise a method for classifying the
boundaries of amplituhedra for any loop order L and helicity k. We determine the branch points
of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations
and are led thereby to a conjecture for the symbol alphabets of all such amplitudes. The study
of amplituhedra is then pushed beyond the realm of N = 4 SYM theory. We provide an efficient
recursive formula to compute the canonical forms of arbitrary d-dimensional simple polytopes, and
illustrate our method via an application to Stokes polytopes, related to scalar theory with quartic coupling.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01085105")
- Topic
- Quantum field theory
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00946584")
- Topic
- Graph theory
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01070819")
- Topic
- Polytopes
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20200720
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations