Space – Time – Matter: Analytic and Geometric Structures

Published by De Gruyter 2018

Space – Time – Matter

Analytic and Geometric Structures

Edited by: Jochen Brüning and Matthias Staudacher
With contributions by: Bernold Fiedler , Klaus Ecker , Friederike Dittberner , Christian Bär , Lars Andersson , Jochen Brüning , Dorothee Schüth , Helga Baum , Andreas Juhl , Klaus Altmann , Gavril Farkas , Schmitt Alexander , Björn Andreas , Dirk Kreimer , Dhritiman Nandan , Valentina Fiorini , Pedro Liendo , Marco Chiodaroli , Livia Ferro , Juliette Hell , Marco Varisco , Sebastian Boldt , Gang Yang , Jan Plefka , Bei Francesco , Batu Güneysu and Ludewig Matthias

https://doi.org/10.1515/9783110452150

Overview
Contents

About this book

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

A summary of the research of the SFB Space-Time-Matter
Includes recent advances in the mathematical foundations of string theory and cosmology
With contributions from renowned institutes s.a. the Max Planck Institute for Gravitational Physics

Author / Editor information

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

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Introduction Jochen Brüning and Matthias Staudacher Requires Authentication Unlicensed Licensed Download PDF	VII
Algebraic K-theory, assembly maps, controlled algebra, and trace methods A primer and a survey of the Farrell–Jones Conjecture Holger Reich and Marco Varisco Requires Authentication Unlicensed Licensed Download PDF	1
Lorentzian manifolds with special holonomy – Constructions and global properties Helga Baum Requires Authentication Unlicensed Licensed Download PDF	51
Contributions to the spectral geometry of locally homogeneous spaces Sebastian Boldt and Dorothee Schueth Requires Authentication Unlicensed Licensed Download PDF	69
On conformally covariant differential operators and spectral theory of the holographic Laplacian Andreas Juhl Requires Authentication Unlicensed Licensed Download PDF	90
Moduli and deformations Global and local investigations in algebraic geometry Klaus Altmann and Gavril Farkas Requires Authentication Unlicensed Licensed Download PDF	116
Vector bundles in algebraic geometry and mathematical physics Björn Andreas and Alexander Schmitt Requires Authentication Unlicensed Licensed Download PDF	150
Dyson–Schwinger equations: Fix-point equations for quantum fields Dirk Kreimer Requires Authentication Unlicensed Licensed Download PDF	186
Hidden structure in the form factors of N = 4 SYM Dhritiman Nandan and Gang Yang Requires Authentication Unlicensed Licensed Download PDF	197
On regulating the AdS superstring Valentina Forini Requires Authentication Unlicensed Licensed Download PDF	221
Constraints on CFT observables from the bootstrap program Pedro Liendo Requires Authentication Unlicensed Licensed Download PDF	245
Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Marco Chiodaroli Requires Authentication Unlicensed Licensed Download PDF	266
Yangian symmetry inmaximally supersymmetric Yang-Mills theory Livia Ferro, Jan Plefka and Matthias Staudacher Requires Authentication Unlicensed Licensed Download PDF	288
Wave and Dirac equations on manifolds Lars Andersson and Christian Bär Requires Authentication Unlicensed Licensed Download PDF	324
Geometric analysis on singular spaces Francesco Bei, Jochen Brüning, Batu Güneysu and Matthias Ludewig Requires Authentication Unlicensed Licensed Download PDF	349
Singularities and long-time behavior in nonlinear evolution equations and general relativity Klaus Ecker and Bernold Fiedler Requires Authentication Unlicensed Licensed Download PDF	417
Index Requires Authentication Unlicensed Licensed Download PDF	491

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate students and researchers in mathematics and physics.
Pages
- Front matter: 22
- Main content: 495
Keywords: Mathematical physics; string theory; cosmology; quantum field theory; algebraic geometry; differential geometry

eBook

Published: April 9, 2018
ISBN: 9783110452150

Hardcover

Published: April 9, 2018
ISBN: 9783110451351