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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01rx913q02p
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dc.contributor.advisorArkani-Hamed, Nimaen_US
dc.contributor.authorTrnka, Jaroslaven_US
dc.contributor.otherPhysics Departmenten_US
dc.date.accessioned2013-09-16T17:26:12Z-
dc.date.available2013-09-16T17:26:12Z-
dc.date.issued2013en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01rx913q02p-
dc.description.abstractQuantum field theory (QFT) is our central theoretical framework to describe the microscopic world, arising from the union of quantum mechanics and special relativity. Since QFTs play such a central role in our understanding of Nature, a deeper study of their physical properties is one of the most exciting directions of research in theoretical physics. This has led to the discovery of many important theoretical concepts, such as supersymmetry and string theory. One of the most prominent physical observable in any QFT is the scattering amplitude, which describes scattering processes of elementary particles. Theoretical progress in understanding and computing scattering amplitudes has accelerated in last few years with the discovery of amazing new mathematical structures in a close cousin of QCD, known as N=4 Super-Yang-Mills theory (SYM). In the first chapter we study integrands of loop amplitudes in planar N=4 SYM and show their astonishing simplicity when written in terms of special set of chiral integrals. In chapter two we show how to reconstruct the multi-loop integrand recursively starting from tree-level amplitudes. This approach makes the long-hidden Yangian symmetry of the theory completely manifest and provides a Lagrangian-independent approach for determining the integrand at any loop order. In chapter three we demonstrate that the problem of calculating of scattering amplitudes in planar N=4 SYM can be completely reformulated in a new framework in terms of on-shell diagrams and integrals over the positive Grassmannian G(k,n). Remarkably, the building blocks for amplitudes play a fundamental role in an active area of research in mathematics spanning algebraic geometry to combinatorics. In chapter four we sketch the argument that the amplitude itself is represented by a single geometrical object defined purely using a new striking property -- positivity -- and all physical concepts like unitarity and locality emerge as derived concepts, each having a sharp geometric interpretation.en_US
dc.language.isoenen_US
dc.publisherPrinceton, NJ : Princeton Universityen_US
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the <a href=http://catalog.princeton.edu> library's main catalog </a>en_US
dc.subjectGrassmannianen_US
dc.subjectN=4 SYMen_US
dc.subjectOn-shell diagramsen_US
dc.subjectScattering Amplitudesen_US
dc.subject.classificationTheoretical physicsen_US
dc.titleGrassmannian Origin of Scattering Amplitudesen_US
dc.typeAcademic dissertations (Ph.D.)en_US
pu.projectgrantnumber690-2143en_US
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