B. Delamotte
Title: An introduction to Non-Perturbative RG
Abstract: I review in these two-hour lectures the basic ideas underlying
Non Perturbative RG (NPRG) and give some methodological insights and
physical results. Among others, I shall particularly focus on the
following questions: What does renormalizability mean from the NPRG
viewpoint? What can do NPRG that perturbative RG cannot? What are the
different approximation methods at our disposal within NPRG (derivative
expansion and BMW method)? What are their limitations? Can we find
genuinely nonperturbative results thanks to NPRG?
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S. Floerchinger
Title: Ultracold quantum gases and functional renormalization
Abstract: I discuss how the functional renormalization group method can be
used to study ultracold quantum gases in homogeneous space. Applications
include attractive fermions with two and three spin components and
repulsive bosons in three and two space dimensions.
I describe in a concrete way how one can construct useful truncations, how
one obtains the corresponding flow equations, how they are solved and how
one can extract interesting information about few-body observables, the
many-body phase diagram and thermodynamic observables from these
solutions. I put emphasis on the special character of nonrelativistic
quantum field theory.
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C. Honerkamp
Title: Functional RG for correlated electrons on two-dimensional lattices:
Abstract: The functional RG approach has become a widely used tool for the
analysis of instabilities in correlated electron systems.
Here we review how approach is used to explore the physics of
interacting electrons on two-dimensional lattices. We describe recent
examples from the fields of pnictide superconductivity and topological
insulators. We will also discuss some interesting directions and
questions for the further development of the method.
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J. Pawlowski
Title: The ERG approach to gauge theories and applications to QCD
Abstract: I review the ERG approach to gauge theories, and its
application to the phase diagram of QCD.
(i) The ERG approach to gauge theories either deforms the gauge symmetry
leading to modified symmetry identities
(modified BRST/Slavnov-Taylor/Ward-Takahashi identities) or implements a
non-local regularisation. I will discuss the pro's and con's of different
implementations.
(ii) In its gauge-fixed form much progress has been achieved in the past
decade both in pure Yang-Mills theories as well as in full QCD. I will
review computations on chiral symmetry breaking and confinement at
vanishing and finite temperature and density. At vanishing density the
results are in quantitative agreement with that obtained with other
methods, in particular the lattice. At finite density, the ERG and
other functional methods offer at present the only ab initio
method for the computation of QCD Green functions.
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M. Reuter
Title: Functional RG Equations in Quantum Gravity
Abstract: In this lecture the specific difficulties will be
discussed which one faces in trying to define a
coarse graining flow for quantum gravity. In
particular the key requirement of background
independence is addressed, and the Asymptotic
Safety program for the nonperturbative
renormalization of Quantum Einstein Gravity is
described.
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C. Wetterich
Title: Emergence of new laws with functional renormalization
Abstract: Physical laws are often qualitatively different on different length
scales. We discuss how new "macroscopic laws" can emerge from more
fundamental "microscopic laws" due to the functional renormalization flow.
This covers the effective "integrating out of degrees of freedom" , "partial
bosonization or fermionization" and "switching to new degrees of freedom"
during the continuous flow.
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