Fauser / Tolksdorf / Zeidler Quantum Field Theory

Competitive Models
1. Auflage 2009
ISBN: 978-3-7643-8736-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 436 Seiten

The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.

Autoren/Hrsg.

Fauser, Bertfried

Tolksdorf, Jürgen

Zeidler, Eberhard

Inhaltsverzeichnis

1;CONTENTS;5
2;Preface;12
3;Constructive Use of Holographic Projections;19
3.1;1. Historical background and present motivations for holography;19
3.2;2. Lightfront holography, holography on null-surfaces and the origin of the area law;22
3.3;3. From holography to correspondence: the AdS/CFT correspondence and a controversy;32
3.4;4. Concluding remarks;40
3.5;Acknowledgements;41
3.6;References;41
4;Topos Theory and ‘Neo-Realist’ Quantum Theory;43
4.1;1. Introduction;43
4.2;2. A formal language for physics;49
4.3;3. The context category V(R) and the topos of presheaves SetV(R)op;51
4.4;4. Representing L(S) in the presheaf topos SetV(R)op;53
4.5;5. Truth objects and truth-values;56
4.6;6. Conclusion and outlook;63
4.7;Acknowledgements;63
4.8;References;64
5;A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications;66
5.1;1. Introduction;66
5.2;2. The mathematical realization of Feynman path integrals;69
5.3;3. Applications;73
5.4;Acknowledgements;79
5.5;References;79
6;A Comment on the Infra-Red Problem in the AdS/ CFT Correspondence;84
6.1;1. Introduction;84
6.2;2. Functional integrals on AdS;85
6.3;3. Two generating functionals;88
6.4;4. The infra-red problem and triviality;92
6.5;5. Conclusions and outlook;96
6.6;References;97
7;Some Steps Towards Noncommutative Mirror Symmetry on the Torus;99
7.1;1. Introduction;99
7.2;2. Elliptic curves;100
7.3;3. Noncommutative elliptic curves;101
7.4;4. Exotic deformations of the Fukaya category;104
7.5;5. Conclusion and outlook;107
7.6;Acknowledgements;108
7.7;References;108
8;Witten’s Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions;111
8.1;1. Introduction;111
8.2;2. Background about moduli space;117
8.3;3. Volume of the moduli space of SU(2) flat connections;119
8.4;4. Volume of the moduli space of flat SU(3) connections;122
8.5;5. Cohomological pairings of the moduli space;124
8.6;References;130
9;Noncommutative Field Theories from a Deformation Point of View;133
9.1;1. Introduction;133
9.2;2. Noncommutative space-times;134
9.3;3. Matter fields and deformed vector bundles;137
9.4;4. Deformed principal bundles;141
9.5;5. The commutant and associated bundles;146
9.6;References;149
10;Renormalization of Gauge Fields using Hopf Algebras;152
10.1;1. Introduction;152
10.2;2. Preliminaries on perturbative quantum field theory;154
10.3;3. The Hopf algebra of Feynman graphs;158
10.4;4. The Hopf algebra of Green’s functions;162
10.5;Appendix A. Hopf algebras;167
10.6;References;168
11;Not so Non-Renormalizable Gravity;170
11.1;1. Introduction;170
11.2;2. The structure of Dyson–Schwinger Equations in QED4;171
11.3;3. Gravity;174
11.4;References;176
12;The Structure of Green Functions in Quantum Field Theory with a General State;178
12.1;1. Introduction;178
12.2;2. Expectation value of Heisenberg operators;180
12.3;3. QFT with a general state;181
12.4;4. Nonperturbative equations;183
12.5;5. Determination of the ground state;186
12.6;6. Conclusion;187
12.7;References;188
13;The Quantum Action Principle in the Framework of Causal Perturbation Theory;191
13.1;1. Introduction;191
13.2;2. The off-shell Master Ward Identity in classical field theory;193
13.3;3. Causal perturbation theory;196
13.4;4. Proper vertices;198
13.5;5. The Quantum Action Principle;200
13.6;6. Algebraic renormalization;208
13.7;References;209
14;Plane Wave Geometry and Quantum Physics;211
14.1;1. Introduction;211
14.2;2. A brief introduction to the geometry of plane wave metrics;212
14.3;3. The Lewis–Riesenfeld theory of the time-dependent quantum oscillator;221
14.4;4. A curious equivalence between two classes of Yang-Mills actions;225
14.5;References;229
15;Canonical Quantum Gravity and Effective Theory;231
15.1;1. Loop quantum gravity;231
15.2;2. Effective equations;234
15.3;3. A solvable model for cosmology;239
15.4;4. Effective quantum gravity;245
15.5;References;246
16;From Discrete Space-Time toMinkowski Space: Basic Mechanisms, Methods and Perspectives;249
16.1;1. Introduction;249
16.2;2. Fermion systems in discrete space-time;250
16.3;3. A variational principle;252
16.4;4. A mechanism of spontaneous symmetry breaking;254
16.5;5. Emergence of a discrete causal structure;257
16.6;6. A first connection to Minkowski space;259
16.7;7. A static and isotropic lattice model;263
16.8;8. Analysis of regularization tails;266
16.9;9. A variational principle for the masses of the Dirac seas;268
16.10;10. The continuum limit;270
16.11;11. Outlook and open problems;271
16.12;References;272
17;Towards a q-Deformed Quantum Field Theory;274
17.1;1. Introduction;274
17.2;2. q-Regularization;275
17.3;3. Basic ideas of the mathematical formalism;278
17.4;4. Applications to physics;287
17.5;5. Conclusion;294
17.6;References;294
18;Towards a q-Deformed Supersymmetric Field Theory;297
18.1;1. Introduction;297
18.2;2. Fundamental Algebraic Concepts;299
18.3;3. q-Deformed Superalgebras;302
18.4;4. q-Deformed Superspaces and Operator Representations;305
18.5;Appendix A. q-Analogs of Pauli matrices and spin matrices;310
18.6;References;312
19;L8-Algebra Connections and Applicationsto String- and Chern-Simons n-Transport;315
19.1;1. Introduction;315
19.2;2. The setting and plan;318
19.3;3. Statement of the main results;326
19.4;4. Differential graded-commutative algebra;330
19.5;5. L8-algebras and their String-like extensions;342
19.6;6. L8-algebra Cartan-Ehresmann connections;379
19.7;7. Higher string- and Chern-Simons n-bundles: the lifting problem;394
19.8;8. L8-algebra parallel transport;411
19.9;9. Physical applications: string-, fivebrane- and p-brane structures;426
19.10;Appendix A. Explicit formulas for 2-morphisms of L8-algebras;429
19.11;Acknowledgements;432
19.12;References;432
19.13;Index;437