Post #2854388

#paperOfTheDay "Integrating out Gluons in Flow equations" from 1996 is another early article about the functional renormalization group #frg , but this time applied to #QCD. The article is relatively long and contains many technicalities, but the main idea is the following: Like every #quantumFieldTheory , QCD contains "quantum fluctuations" on every energy scale, which can be integrated out from high to low energy with the help of a renormalization group flow equation. Unlike the scalar field theories that are often studied as toy models, QCD contains two fundamentally different types of fields: The fermions (quarks), which represent matter, and the bosons (gluons), which are particles of the strong force. Now it turns out that one can arrange the flow equations in such a way that only one type of field is (at first) integrated out, and serves as an "input" for the flow of the other. In principle, this would be exact and yield a full solution of QCD (which still today would be a breakthrough in #physics ), but in practice of course one has to use truncations and approximations. In fact, the computations presented in the paper are rather "coarse" and don't really produce new results; the point is rather to establish the method. What is interesting is that here, the gluons are integrated out, and one obtains an effective theory for the interaction of matter. This sounds reasonable, but it is the opposite of how lattice simulations (another well-developed approach at non-perturbative QCD) work: There, the gluon field is being simulated, and the fermions are merely a correction term. https://arxiv.org/abs/hep-ph/9604227