Effective theories in classical and quantum mechanics
Working in quantum many-body theory, I slowly learned that many key concepts and techniques have predecessors and analogues in classical systems and one-body quantum systems. Examples include Green's functions, path integrals, cumulants, the linked cluster theorem, Hubbard-Stratonavich transformation (completing the square), mean-field theory, localisation due to disorder, and BBGKY hierarchy . Learning a full-blown quantum many-body version is easier if you first understand simpler analogues. This post is about effective theories in classical systems and one-body quantum systems, following my earlier post about effective theories in quantum field theories of elementary particles . Michèle Levi has a pedagogical article Effective field theories of post-Newtonian gravity: a comprehensive review This is motivated by the use of EFTs to describe gravitational waves produced by the inspiraling and merging of binary black holes and neutron stars . She discusses the different scales invo