{"product_id":"grassmannian-geometry-of-scattering-amplitudes-hardback-9781107086586","title":"Grassmannian Geometry of Scattering Amplitudes (Hardback) 9781107086586","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eGrassmannian Geometry of Scattering Amplitudes\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAn essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eNima Arkani-Hamed (Author), Jacob Bourjaily (Author), Freddy Cachazo (Author), Alexander Goncharov (Author), Alexander Postnikov (Author), Jaroslav Trnka (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107086586, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 5 May 2016\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e201 pages, 192 b\/w illus.  8 tables\u003cbr\u003e25.3 x 18 x 1.4 cm, 0.56 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This book is the 'Diagrammar' of the twenty-first century. Just as Gerard 't Hooft and Martinus Veltman laid out in 1973 the then-new calculus of Feynman diagrams for scattering processes in non-abelian gauge theories, so now have Nima Arkani-Hamed and his co-authors set forth a new perspective on scattering amplitudes, which leads away from locality and unitarity toward other principles, and they have provided a detailed and elegantly illustrated how-to manual for the practitioner.' Lance Dixon, Stanford University\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eOutlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eAcknowledgements\u003cbr\u003e 1. Introduction\u003cbr\u003e 2. Introduction to on-shell functions and diagrams\u003cbr\u003e 3. Permutations and scattering amplitudes\u003cbr\u003e 4. From on-shell diagrams to the Grassmannian\u003cbr\u003e 5. Configurations of vectors and the positive Grassmannian\u003cbr\u003e 6. Body configurations, graphs, and permutations\u003cbr\u003e 7. The invariant top-form and the positroid stratification\u003cbr\u003e 8. (Super) conformal and dual conformal invariance\u003cbr\u003e 9. Positive diffeomorphisms and Yangian invariance\u003cbr\u003e 10. The kinematical support of physical on-shell forms\u003cbr\u003e 11. Homological identities among Yangian-invariants\u003cbr\u003e 12. (Relatively) orienting canonical coordinate charts on positroids\u003cbr\u003e 13. Classification of Yangian-invariants and their relations\u003cbr\u003e 14. The Yang–Braxter relation and ABJM theories\u003cbr\u003e 15. On-shell diagrams for theories with N\u0026lt;4 supersymmetries\u003cbr\u003e 16. Dual graphs and cluster algebras\u003cbr\u003e 17. On-shell representations of scattering amplitudes\u003cbr\u003e 18. Outlook\u003cbr\u003e References.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical physics [\u003ca title=\"See our other books on Mathematical physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20physics%20%5BPHU%5D%22\"\u003ePHU\u003c\/a\u003e], Particle \u0026amp; high-energy physics [\u003ca title=\"See our other books on Particle \u0026amp; high-energy physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Particle%20\u0026amp;%20high-energy%20physics%20%5BPHP%5D%22\"\u003ePHP\u003c\/a\u003e], Physics [\u003ca title=\"See our other books on Physics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Physics%20%5BPH%5D%22\"\u003ePH\u003c\/a\u003e], Mathematics \u0026amp; science [\u003ca title=\"See our other books on Mathematics \u0026amp; science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20\u0026amp;%20science%20%5BP%5D%22\"\u003eP\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46002993987864,"sku":"9781107086586","price":58.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107086586i_e0d5a10d-f1a3-490b-b8eb-90906d97970e.jpg?v=1696792066","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/grassmannian-geometry-of-scattering-amplitudes-hardback-9781107086586","provider":"Freshly Printed Books","version":"1.0","type":"link"}