When systems of particles interact strongly, their few- and many-body properties can exhibit some highly non-trivial phenomenology that is absent in their weakly-coupled and non-interacting counterparts. Remarkable effects range from the Efimov effect, to the transition from molecule to "dressed" single particle (polaron) when an impurity is embedded in a Fermi gas. The description of strong interactions is very challenging since perturbation theory, so successful in describing many fundamental phenomena (e.g. in Quantum Electrodynamics), is of no use. Here is where few-body physics can be of great aid, since many few-body problems can be accurately solved and, moreover, can be cleverly related to the many-body problem in a large variety of problems.
This book presents a detailed account of the theory and methods to tackle the aforementioned systems from a bottom-up approach, which has been largely developed in the past decade by the authors and other experts in the field. This begins with a full characterisation of strongly interacting few-particle systems, which can be dealt with accurately using a variety of analytical and numerical techniques. These non-perturbative solutions can be used to gain qualitative and quantitative insight into more complex problems, especially the many-body problem. The book gives a detailed overview of the relevant and current research literature in the field, and is a valuable tool for researchers and graduate students.
