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Instructors: Univ.-Prof. Dr. Martin Reuter
Event type:
Lecture/practice class
Displayed in timetable as:
Hours per week:
4
Credits:
6,0
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Requirements / organisational issues:
Contents:
Functional Renormalization Group Equations are an important modern approach to the non-perturbative construction and investigation of statistical and quantum field theories. Their scope extends far beyond the traditional domain of renormalization ("elimination of infinities"), being a tool which in principle allows to completely "solve" the theory.
This lecture aims at introducing the prerequisites of this approach in an elementary fashion, to outline its general properties, and to discuss some selected applications, including a brief outlook at non-perturbatively renormalized Quantum Einstein Gravity.
Topics will include: Elements of quantum field theory and statistical mechanics, the functional Schrödinger picture, functional differential equations à la Schwinger-Symanzik and functional integrals à la Feynman, effective actions, lattice field theory, Wilsonian renormalization group, continuum-based flow equations, critical phenomena, forms of non-perturbative UV limits, applications.
Remark: While helpful clearly, familiarity with the first lecture course of this series in WS 2023/24, is not assumed.
Recommended reading list:
- R. J. Rivers, Path Integral Methods in Quantum Field Theory, Cambridge University Press
- A. Das, Field Theory - A Path Integral Approach, World Scientific
- J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford University Press
- M. Le Bellac, Quantum and Statistical Field Theory, Oxford Univeristy Press
- A. Wipf, Statistical Approach to Quantum Field Theory, Springer
- M. Reuter and F. Saueressig, Quantum Gravity and the Functional Renormalization Group, Cambridge University Press
- A. Ashtekar, M. Reuter and C. Rovelli, arXiv:1408.4336
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