Fundamental problems in quantum field theory at high temperature

In this work, the author studies two fundamental problems in relativistic quantum field theory. He investigates supersymmetry at positive temperature. A modified O'Raifeartaigh model, which has a supersymmetry and no other symmetry, is considered. At zero temperature the supersymmetry is spontaneously broken. The one-loop self-energy corrections to the fermion mass matrix is calculated. He finds that supersymmetry is not restored at any temperature in the sense that no phase transitions occur and in the sense that the zero temperature Goldstone fermion remains massless at all temperatures. The massless scalar field lambdaphi4 theory at finite temperature is investigated. At T > 0 the partition function and the scalar boson mass have a non-analytic behavior in the weak coupling expansion of lambda, which is known as plasmon effect. The author evaluates the one-loop corrections of the vertex function. It is found that there is an indication that a screening effect takes place. At high temperature it is found that the imaginary part of the vertex function in the s-channel has a nonanalytic behavior in lambda and is weakly temperature dependent