Ebook: Quantum Field Theory: Competitive Models

For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. 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'.

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For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics.

The present book features some of the different approaches, viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT.

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.

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For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics.

The present book features some of the different approaches, viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT.

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.

Content:
Front Matter....Pages i-xix
Constructive Use of Holographic Projections....Pages 1-24
Topos Theory and ‘Neo-Realist’ Quantum Theory....Pages 25-47
A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications....Pages 49-66
A Comment on the Infra-Red Problem in the AdS/CFT Correspondence....Pages 67-81
Some Steps Towards Noncommutative Mirror Symmetry on the Torus....Pages 83-94
Witten’s Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions....Pages 95-116
Noncommutative Field Theories from a Deformation Point of View....Pages 117-135
Renormalization of Gauge Fields using Hopf Algebras....Pages 137-154
Not so Non-Renormalizable Gravity....Pages 155-162
The Structure of Green Functions in Quantum Field Theory with a General State....Pages 163-175
The Quantum Action Principle in the Framework of Causal Perturbation Theory....Pages 177-196
Plane Wave Geometry and Quantum Physics....Pages 197-216
Canonical Quantum Gravity and Effective Theory....Pages 217-234
From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives....Pages 235-259
Towards a q-Deformed Quantum Field Theory....Pages 261-283
Towards a q-Deformed Supersymmetric Field Theory....Pages 285-302
L ?-Algebra Connections and Applications to String- and Chern-Simons n-Transport....Pages 303-424
Back Matter....Pages 425-436

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For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics.

The present book features some of the different approaches, viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT.

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.

Content:
Front Matter....Pages i-xix
Constructive Use of Holographic Projections....Pages 1-24
Topos Theory and ‘Neo-Realist’ Quantum Theory....Pages 25-47
A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications....Pages 49-66
A Comment on the Infra-Red Problem in the AdS/CFT Correspondence....Pages 67-81
Some Steps Towards Noncommutative Mirror Symmetry on the Torus....Pages 83-94
Witten’s Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions....Pages 95-116
Noncommutative Field Theories from a Deformation Point of View....Pages 117-135
Renormalization of Gauge Fields using Hopf Algebras....Pages 137-154
Not so Non-Renormalizable Gravity....Pages 155-162
The Structure of Green Functions in Quantum Field Theory with a General State....Pages 163-175
The Quantum Action Principle in the Framework of Causal Perturbation Theory....Pages 177-196
Plane Wave Geometry and Quantum Physics....Pages 197-216
Canonical Quantum Gravity and Effective Theory....Pages 217-234
From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives....Pages 235-259
Towards a q-Deformed Quantum Field Theory....Pages 261-283
Towards a q-Deformed Supersymmetric Field Theory....Pages 285-302
L ?-Algebra Connections and Applications to String- and Chern-Simons n-Transport....Pages 303-424
Back Matter....Pages 425-436
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