ABSTRACT
This chapter discusses field theories at finite temperature along with the study of the equilibrium thermodynamic properties. A subtlety which arises for gauge fields is that there are only two independent degrees of freedom for a massless vector field, but in a typical renormalisable gauge the Lagrangian involves four degrees of freedom. The two extra degrees of freedom are not physical and cannot be in equilibrium with a heat bath. There are also the Faddeev–Popov ghosts, which do not correspond to physical particles and lead to the same difficulty. The chapter discusses the generation of functionals for temperature Green functions which contain information about the equilibrium thermodynamic properties of the finite temperature system and have no time dependence. It describes the Higgs model, which incorporates both scalar and vector fields, to study finite temperature. The chapter also constructs the finite temperature effective potential for the grand unified theory.
