Polytopes, scattering amplitudes, and cohomology
<p>We introduce a new definition of abstract polytope in any dimension and answer the question of defining and calculating its area. The entire discussion is motivated by studying the expressions arising from super-BCFW recursion on tree-level, <em>n</em>-point NMHV amplitudes in...
| Päätekijä: | |
|---|---|
| Muut tekijät: | |
| Aineistotyyppi: | Opinnäyte |
| Kieli: | English |
| Julkaistu: |
2014
|
| Aiheet: |
| _version_ | 1826264165756436480 |
|---|---|
| author | Enciso, M |
| author2 | Hodges, A |
| author_facet | Hodges, A Enciso, M |
| author_sort | Enciso, M |
| collection | OXFORD |
| description | <p>We introduce a new definition of abstract polytope in any dimension and answer the question of defining and calculating its area. The entire discussion is motivated by studying the expressions arising from super-BCFW recursion on tree-level, <em>n</em>-point NMHV amplitudes in the planar limit of <em>N</em>=4 Super Yang-Mills (SYM) theory. It has recently been discovered that such expressions should be interpreted as volumes of complex projective polytopes in some sense, and here we give this interpretation explicit meaning. In doing so, we uncover a novel calculus for calculating the volumes of such polytopes. This calculus can be used on the polytopes corresponding to these BCFW representations of amplitudes to obtain new expressions that make manifest all of the known properties of the polytopes. Additionally, we show how this new calculus can be used to readily obtain the volumes of any lower-dimensional face of an arbitrary polytope.</p> <p>We begin by reviewing the known results for <em>n</em>-point NMHV amplitudes in planar <em>N</em>=4 SYM. In Chapter 2 we introduce our new definition of abstract (oriented) polytopes in terms of new objects called cyclic lists, and in Chapter 3 we define the volumes of these polytopes using cyclic lists in a natural way. Chapter 4 introduces a useful calculus for calculating not only the volumes of these polytopes, but also the volumes of any of their lower dimensional bounding polytopes. Finally, in Chapter 5, we briefly explore the twistor and cohomology theory that motivates the calculus and which may provide important insight for generalization of this whole discussion to more exotic spaces.</p> |
| first_indexed | 2024-03-06T20:03:23Z |
| format | Thesis |
| id | oxford-uuid:2817e2b7-c356-4fb9-9cdd-24a4099fa0bd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:03:23Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:2817e2b7-c356-4fb9-9cdd-24a4099fa0bd2022-03-26T12:10:46ZPolytopes, scattering amplitudes, and cohomologyThesishttp://purl.org/coar/resource_type/c_bdccuuid:2817e2b7-c356-4fb9-9cdd-24a4099fa0bdScattering AmplitudesPolytopesMathematical PhysicsEnglishOxford University Research Archive - Valet2014Enciso, MHodges, APenrose, R<p>We introduce a new definition of abstract polytope in any dimension and answer the question of defining and calculating its area. The entire discussion is motivated by studying the expressions arising from super-BCFW recursion on tree-level, <em>n</em>-point NMHV amplitudes in the planar limit of <em>N</em>=4 Super Yang-Mills (SYM) theory. It has recently been discovered that such expressions should be interpreted as volumes of complex projective polytopes in some sense, and here we give this interpretation explicit meaning. In doing so, we uncover a novel calculus for calculating the volumes of such polytopes. This calculus can be used on the polytopes corresponding to these BCFW representations of amplitudes to obtain new expressions that make manifest all of the known properties of the polytopes. Additionally, we show how this new calculus can be used to readily obtain the volumes of any lower-dimensional face of an arbitrary polytope.</p> <p>We begin by reviewing the known results for <em>n</em>-point NMHV amplitudes in planar <em>N</em>=4 SYM. In Chapter 2 we introduce our new definition of abstract (oriented) polytopes in terms of new objects called cyclic lists, and in Chapter 3 we define the volumes of these polytopes using cyclic lists in a natural way. Chapter 4 introduces a useful calculus for calculating not only the volumes of these polytopes, but also the volumes of any of their lower dimensional bounding polytopes. Finally, in Chapter 5, we briefly explore the twistor and cohomology theory that motivates the calculus and which may provide important insight for generalization of this whole discussion to more exotic spaces.</p> |
| spellingShingle | Scattering Amplitudes Polytopes Mathematical Physics Enciso, M Polytopes, scattering amplitudes, and cohomology |
| title | Polytopes, scattering amplitudes, and cohomology |
| title_full | Polytopes, scattering amplitudes, and cohomology |
| title_fullStr | Polytopes, scattering amplitudes, and cohomology |
| title_full_unstemmed | Polytopes, scattering amplitudes, and cohomology |
| title_short | Polytopes, scattering amplitudes, and cohomology |
| title_sort | polytopes scattering amplitudes and cohomology |
| topic | Scattering Amplitudes Polytopes Mathematical Physics |
| work_keys_str_mv | AT encisom polytopesscatteringamplitudesandcohomology |