Aspects of Scattering Amplitudes and Moduli Space Localization

AvSebastian Mizera

Inbunden, Engelska, 2020

Del i serien Springer Theses

1 102 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

E-bok

1 413 kr

Häftad

1 102 kr

Beskrivning

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 toscattering 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.

Produktinformation

Utgivningsdatum:2020-09-24
Mått:155 x 235 x 14 mm
Vikt:358 g
Format:Inbunden
Språk:Engelska
Serie:Springer Theses
Antal sidor:134
Upplaga:20001
Förlag:Springer Nature Switzerland AG
ISBN:9783030530099

Utforska kategorier

Matematik inom Naturvetenskap och teknik
Fysik inom Naturvetenskap och teknik
Matematisk fysik inom Naturvetenskap och teknik

Mer om författaren

Dr. Sebastian Mizera is a member at the Institute for Advanced Study in Princeton, NJ. He graduated from the University of Cambridge with a bachelor's degree in natural sciences and a master's in mathematics. He obtained a PhD in theoretical physics from the Perimeter Institute and the University of Waterloo in Canada. Dr. Mizera's work focuses on the interconnections between scattering amplitudes in quantum field theories and the mathematics of algebraic geometry and topology.

Innehållsförteckning

Chapter1: Introduction.- Chapter2: Intersection Numbers of Twisted Di erential Forms.- Chapter3: Recursion Relations from Braid Matrices.- Chapter4: Further Examples of Intersection Numbers.- Chapter5: Conclusion.

Mer från samma författare

What is the iε for the S-matrix?

Holmfridur Sigridar Hannesdottir, Sebastian Mizera

Häftad, 2023

609 kr

What is the ie for the S-matrix?

Sebastian Mizera, Holmfridur Sigridar Hannesdottir

E-bok

2023

797 kr

Del 1041

Records from the S-Matrix Marathon

Nima Arkani-Hamed, Mathieu Giroux, Holmfridur Sigridar Hannesdottir, Sebastian Mizera, Celina Pasiecznik

Häftad, 2025

1 211 kr

Records from the S-Matrix Marathon

Celina Pasiecznik, Sebastian Mizera, Holmfridur Sigridar Hannesdottir, Mathieu Giroux, Nima Arkani-Hamed

E-bok

Jeffrey Michael McMahon

Inbunden, 2011

1 102 kr

Du kanske också är intresserad av

Pokémon Pokémon Mega Evolution 05 - Pitch Black Booster

Pokémon

79 kr