Mathematical Structures of the Universe

Table of Contents

 

Michał Eckstein, Michael Heller, Sebastian J. Szybka

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Part I

General Relativity and Cosmology

 

Manuel Hohmann

Observer dependent geometries . . . . . . . . . . . . . . . . . . . . . 13

 

Krzysztof Drachal &Wiesław Sasin

Classi_cation of classical singularities: a di_erential spaces approach . . 57

 

Jacek Gruszczak

The smooth beginning of the Universe . . . . . . . . . . . . . . . . . . 69

 

Mariusz P. Dabrowski

Are singularities the limits of cosmology? . . . . . . . . . . . . . . . . . 101

 

Boudewijn F. Roukema

Simplicity in cosmology: add virialisation, remove _, keep classical GR . 119

 

AndrzejWoszczyna & Zdzisław A. Golda

Computer algebra tests physical theories:

the case of relativistic astrophysics . . . . . . . . . . . . . . . . . . . . 127

 

Sebastian J. Szybka

On gravitational interactions between two bodies . . . . . . . . . . . . 137

Quantum Geometries

 

Marek Kus

Geometry of quantum correlations . . . . . . . . . . . . . . . . . . . . 155

 

Jordan François, Serge Lazzarini & Thierry Masson

Gauge _eld theories: various mathematical approaches . . . . . . . . . 177

 

Harald Grosse & RaimarWulkenhaar

Towards a construction of a quantum _eld theory in four dimensions . 227

 

Mairi Sakellariadou

Unweaving the fabric of the Universe:

the interplay between mathematics and physics . . . . . . . . . . . . . 259

 

Jerzy Lukierski

Quantum gravity models – a brief conceptual summary . . . . . . . . . 277

 

Andrzej Sitarz

Pointless geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

 

Nicolas Franco &Michał Eckstein

Noncommutative geometry, Lorentzian structures and causality . . . . 315

 

Michael Heller & Dominique Lambert

Ontology and noncommutative geometry . . . . . . . . . . . . . . . . 341

Part III

Overviews

 

Shahn Majid

The self-representing Universe . . . . . . . . . . . . . . . . . . . . . . . 357

 

Malcolm A.H. MacCallum

Re_ections on the geometrization of physics . . . . . . . . . . . . . . . 389

 

Bernard Carr

Metacosmology and the limits of science . . . . . . . . . . . . . . . . . 407

 

Jerzy Kowalski-Glikman

The price for mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 433

 

Michael Heller

The _eld of rationality and category theory . . . . . . . . . . . . . . . . 441