Many-Body Formalism

Abstract

As already noted in Chapter 39, systems of many identical particles, either bosons or fermions, form an important part of nature and, because of the required overall symmetry or antisymmetry of the many-particle wave function, these form not only important, but also very special, types of quantum-mechanical systems. Examples we have met are the many-electron system of an atom, or the many-electron system of condensed matter physics, the many nucleon-system of a nucleus, and the rnany-quark system of particle physics, All of these involve identical spin 1/2 particles and, hence, fermions. All of these identical particles have besides their orbital degrees of freedom, internal degrees of freedom such as their spin degree of freedom, but in the case of identical nucleons, an additional charge or isospin internal degree of freedom, and in the case of quarks, additional flavor (including isospin) and color degrees of freedom. Systems of identical bosons include the system of many 4He atoms, an example of a many-particle system where we may be dealing with a huge number of identical particles. Other examples of many-boson systems would include more complicated atoms, provided the identical atoms have an electron plus nucleon number that is an even number so the total atomic spin is an integer. Such systems are of particular recent interest in connection with the Bose—Einstein condensation of such atomic gases.