Aspects Of Scattering Amplitudes And Moduli Space Localization

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Aspects Of Scattering Amplitudes And Moduli Space Localization

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Author : Sebastian Mizera
language : en
Publisher: Springer Nature
Release Date : 2020-09-23

Aspects Of Scattering Amplitudes And Moduli Space Localization written by Sebastian Mizera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Science categories.

This thesis proposes a new perspective on scattering amplitudes in quantum field theories. Their standard formulation in terms of sums over Feynman diagrams is replaced by a computation of geometric invariants, called intersection numbers, on moduli spaces of Riemann surfaces. It therefore gives a physical interpretation of intersection numbers, which have been extensively studied in the mathematics literature in the context of generalized hypergeometric functions. This book explores physical consequences of this formulation, such as recursion relations, connections to geometry and string theory, as well as a phenomenon called moduli space localization. After reviewing necessary mathematical background, including topology of moduli spaces of Riemann spheres with punctures and its fundamental group, the definition and properties of intersection numbers are presented. A comprehensive list of applications and relations to other objects is given, including those to scattering amplitudes in open- and closed-string theories. The highlights of the thesis are the results regarding localization properties of intersection numbers in two opposite limits: in the low- and the high-energy expansion. In order to facilitate efficient computations of intersection numbers the author introduces recursion relations that exploit fibration properties of the moduli space. These are formulated in terms of so-called braid matrices that encode the information of how points braid around each other on the corresponding Riemann surface. Numerous application of this approach are presented for computation of scattering amplitudes in various gauge and gravity theories. This book comes with an extensive appendix that gives a pedagogical introduction to the topic of homologies with coefficients in a local system.

Anti Differentiation And The Calculation Of Feynman Amplitudes

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Author : Johannes Blümlein
language : en
Publisher: Springer Nature
Release Date : 2021-11-26

Anti Differentiation And The Calculation Of Feynman Amplitudes written by Johannes Blümlein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-26 with Science categories.

This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.

What Is The I For The S Matrix

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Author : Holmfridur Sigridar Hannesdottir
language : en
Publisher: Springer Nature
Release Date : 2023-01-01

What Is The I For The S Matrix written by Holmfridur Sigridar Hannesdottir and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.

This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals.

Continuous Advances In Qcd 2006

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Author : M. Peloso
language : en
Publisher: World Scientific
Release Date : 2007

Continuous Advances In Qcd 2006 written by M. Peloso and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

The volume contains the proceedings of the workshop Continuous Advances in QCD 2006, hosted by the Wiliam I Fine Theoretical Physics Institute. This biennial workshop was the seventh meeting of the series, held at the University of Minnesota since 1994. The workshop gathered together about 110 scientists (a record number for the event), including most of the leading experts in quantum chromodynamics and non-Abelian gauge theories in general.

Continuous Advances In Qcd 2006 Proceedings Of The Conference

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Author : Misha Shifman
language : en
Publisher: World Scientific
Release Date : 2007-03-12

Continuous Advances In Qcd 2006 Proceedings Of The Conference written by Misha Shifman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-12 with Science categories.

The volume contains the proceedings of the workshop Continuous Advances in QCD 2006, hosted by the Wiliam I Fine Theoretical Physics Institute. This biennial workshop was the seventh meeting of the series, held at the University of Minnesota since 1994. The workshop gathered together about 110 scientists (a record number for the event), including most of the leading experts in quantum chromodynamics and non-Abelian gauge theories in general.

Proceedings Of The Conference On Continuous Advances In Qcd 2006

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Author : Marco M. Peloso
language : en
Publisher: World Scientific
Release Date : 2007

Proceedings Of The Conference On Continuous Advances In Qcd 2006 written by Marco M. Peloso and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

The volume contains the proceedings of the workshop Continuous Advances in QCD 2006, hosted by the Wiliam I Fine Theoretical Physics Institute. This biennial workshop was the seventh meeting of the series, held at the University of Minnesota since 1994. The workshop gathered together about 110 scientists (a record number for the event), including most of the leading experts in quantum chromodynamics and non-Abelian gauge theories in general.

Grassmannian Geometry Of Scattering Amplitudes

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Author : Nima Arkani-Hamed
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-05

Grassmannian Geometry Of Scattering Amplitudes written by Nima Arkani-Hamed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.

An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.

Dissertation Abstracts International

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Author :
language : en
Publisher:
Release Date : 2008

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Dissertations, Academic categories.

Topological Geometrodynamics

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Author : Matti Pitkanen
language : en
Publisher: Luniver Press
Release Date : 2006

Topological Geometrodynamics written by Matti Pitkanen and has been published by Luniver Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Topological GeometroDynamics is a modification of general relativity inspired by the conceptual problems related to the definitions of inertial and gravitational energy in general relativity. Topological geometrodynamics can be also seen as a generalization of super string models. Physical space-times are seen as four-dimensional surfaces in certain eight-dimensional space. The choice of this space is fixed by symmetries of the standard model so that geometrization of known classical fields and elementary particle quantum numbers results. The notion of many-sheeted space-time allows re-interpretation of the structures of perceived world in terms of macroscopic space-time topology. The generalization of the number concept based on fusion of real numbers and p-adic number fields implies a further generalization of the space-time concept allowing to identify space-time correlates of cognition and intentionality. Quantum measurement theory extended to a quantum theory of consciousness becomes an organic part of theory. A highly non-trivial prediction is the existence of a fractal hierarchy of copies of standard model physics with dark matter identified in terms of macroscopic quantum phases characterized by dynamical and quantized Planck constant. The book is a comprehensive overview and analysis of topological geometrodynamics as a mathematical and physical theory.

Physics Briefs

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Author :
language : en
Publisher:
Release Date : 1994

Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Physics categories.