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Non-perturbative aspects of gauge theories
Jan Martin Pawlowski
Content of lecture series
In the lecture course modern Renormalisation Group techniques are applied
to strongly-correlated physics in QCD and Quantum Gravity
The lecture course provides an introduction to the stronly-correlated
physics of QCD and Quantum Gravity. The related physics problems are
treated within the Functional Renormalisation Group (FRG), and a survey of
alternative approaches is provided.
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Outline
- Derivation
- Truncation schemes, optimisation & numerics
- Fixed points in the Functional RG
- Introduction
- Confinement & chiral symmetry breaking
- Confinement-deconfinement phase transition at finite T
- A glimpse at the QCD phase diagram
- Introduction
- RG approach to quantum gravity
- Fixed point structure of quantum gravity
- Cosmological applications
| Aoki | Introduction to the Non-perturbative RG | Int.J.Mod.Phys.B14:1249-1326,2000 | |
| Berges, Tetradis, Wetterich | Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics | Phys.Rept.363:223-386,2002 | |
| Polonyi | Lectures on the functional renormalization group method | Central Eur.J.Phys.1:1-71,2003 |
| Litim, Pawlowski | On gauge invariant Wilsonian flows | Proceedings 'The ERG', Word Scientific '99 | |
| Pawlowski | On Wilsonian flows in gauge theories | Habilitation thesis, Erlangen '02 | |
| Pawlowski | Aspects of the FRG | Annals Phys.322:2831-2915,2007 | |
| Gies | Introduction to the FRG and applications to gauge theories | Lecture notes | |
| Reuter, Saueressig | FRG Equations, Asymptotic Safety, and Quantum Einstein Gravity | Lecture notes | |
| Niedermaier, Reuter | The Asymptotic Safety Scenario in Quantum Gravity | Living review |
FRG-reviews on various topics are listed as refs. [15]-[27] in 'Aspects of the FRG' .
| Alkofer, von Smekal | The Infrared Behavior of QCD Green's Functions | Phys.Rept.353:281,2001 | |
| Fischer | Infrared Properties of QCD from Dyson-Schwinger equations | J.Phys.G32:R253-R291,2006 |
Literature, basics
| Amit | Field Theory, the Renormalization Group, and Critical Phenomena | World Scientific | |
| Binney, Dowrick, Fisher, Newman | The Theory of Critical Phenomena, an Introduction to the Renormalization Group | Clarendon Press, Oxford | |
| Cardy | Scaling and Renormalization in Statistical Physics | Cambridge University Press | |
| Collins | Renormalization | Springer | |
| Parisi | Statistical Field Theory | Addison-Wesley | |
| Zinn-Justin | Quantum Field Theory and Critical Phenomena | Claredon Press, Oxford |
| Haag | Local Quantum Physics | Springer, 1996 | |
| Itzykson, Zuber | Quantum Field Theory | McGraw-Hill | |
| Peskin, Schroeder | An Introduction to Quantum Field Theory | Addison Wesley | |
| Siegel | Fields | hep-th/9912205 | |
| Weinberg | The Quantum Theory of Fields, Vol. 1-2 | Cambridge University Press |
| Kugo | Eichtheorie | Springer, 1997 | |
| Miransky | Dynamical Symmetry Breaking in Quantum Field Theories | World Scientific, 1993 | |
| Muta | Foundations of Quantum Chromodynamics | World Scientific, 1987 | |
| Pokorski | Gauge Field Theories | Cambridge, 1987 | |
| Wu-Ki Tung | Group Theory in Physics | World Scientific, 1985 | |
| Zinn-Justin | Quantum Field Theory and Critical Phenomena | Oxford, 1993 |
| Carroll | Spacetime and Geometry | Addison Wesley | |
| Göckeler & Schücker | Differential Geometry, gauge theories, and gravity | Cambridge University Press | |
| Misner, Torne, Wheeler | Graviation | Freeman |
Non-perturbative aspects of gauge theories, Jan Martin Pawlowski
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