Field Theory at finite Temperature and Density: Applications to Quark Stars

Abstract:In this thesis we will consider different thermal field theories, and derive an equation of state for deconfined matter.This equation of state will be used in the Tolman-Oppenheimer-Volkoff (TOV)-equations to calculate the mass andradius of quark stars.Firstly, a scalar field with a four-point interaction is studied at finitie temperature, and the validity of the perturba-tive expansion is discussed. The pressure is calculated to fifth order.Secondly, QED and QCD are studied at finite chemical potential and zero temperature, and an equation of state fordegenerate quark matter is derived.Next, general relativity is discussed, and Einstein s field equations as well as the TOV-equations are derived.These last equations are used to model dense stars with different equations of state, and finally the equation describingdeconfined matter is used to determine the mass-radius relationship for quark stars with different central pressures.The results obtained in this thesis indicate in which range of masses and radii quark stars could be observed, andit is discussed how the models used here could be improved and made more realistic.