Space - Time - Matter: Analytic and Geometric Structures

by Jochen Brüning (Editor), Matthias Staudacher (Editor), Bernold Fiedler (Contribution by), Klaus Ecker (Contribution by), Friederike Dittberner (Contribution by)

Overview

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail.

Contents
Introduction
Algebraic K-theory, assembly maps, controlled algebra, and trace methods
Lorentzian manifolds with special holonomy – Constructions and global properties
Contributions to the spectral geometry of locally homogeneous spaces
On conformally covariant differential operators and spectral theory of the holographic Laplacian
Moduli and deformations
Vector bundles in algebraic geometry and mathematical physics
Dyson–Schwinger equations: Fix-point equations for quantum fields
Hidden structure in the form factors ofN = 4 SYM
On regulating the AdS superstring
Constraints on CFT observables from the bootstrap program
Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities
Yangian symmetry in maximally supersymmetric Yang-Mills theory
Wave and Dirac equations on manifolds
Geometric analysis on singular spaces
Singularities and long-time behavior in nonlinear evolution equations and general relativity

Product Details

ISBN-13:	9783110451351
Publisher:	De Gruyter
Publication date:	04/09/2018
Pages:	517
Product dimensions:	6.69(w) x 9.45(h) x (d)
Age Range:	18 Years

About the Author

Matthias Staudacher and Jochen Brüning, Humboldt-Universität zu Berlin, Germany.

Table of Contents

Introduction Klaus Ecker Bernold Fiedler et al. vii

Algebraic K-theory, assembly maps, controlled algebra, and trace methods Holger Reich Marco Varisco 1

Lorentzian manifolds with special holonomy - Constructions and global properties Helga Baum 51

Contributions to the spectral geometry of locally homogeneous spaces Sebastian Boldt Dorothee Schueth 69

On conformally covariant differential operators and spectral theory of the holographic Laplacian Andreas Juhl 90

Modull and deformations Klaus Altmann Gavril Farkas 116

Vector bundles In algebraic geometry and mathematical physics Björn Andreas Alexander Schmitt 150

Dyson-Schwinger equations: Fix-point equations for quantum fields Dirk Kreimer 186

Hidden structure In the form factors of N = 4 SYM Dhritiman Nandan Gang Yang 197

On regulating the AdS superstring Valentina Forini 221

Constraints on CFT observables from the bootstrap program Pedro Liendo 245

Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Marco Chiodaroli 266

Yangian symmetry in maximally supersymmetric Yang-Mills theory Livia Ferro Jan Plefka Matthias Staudacher 288

Wave and Dirac equations on manifolds Lars Andersson Christian Bär 324

Geometric analysis on singular spaces Francesco Bei Jochen Brüning Batu Güneysu Matthias Ludewig 349

Singularities and long-time behavior in nonlinear evolution equations and general relativity Klaus Ecker Bernold Fiedler et al 417

Index 491