Finite density

Abstract

The concept of a system at a finite density or, equivalently, at a finite chemical potential, is introduced. Considering first a complex scalar field, an imaginary-time path integral representation is derived for the partition function. The evaluation of the partition function reveals infrared problems, which are this time related to the phenomenon of Bose-Einstein condensation. A generic tool applicable to any scalar field theory, called the effective potential, is introduced in order to handle this situation. Subsequently the case of a Dirac fermion at a finite chemical potential is discussed. The concept of a susceptibility is introduced. The quark number susceptibility in QCD is evaluated up to second order in the gauge coupling.