On Effective Field Theories at Finite Temperature

TL;DR

This paper explores effective field theories at finite temperature, focusing on dimensional reduction, renormalization, and applications to spinor and scalar QED, including calculations of screening masses and free energy.

Contribution

It introduces two methods for constructing effective three-dimensional field theories and applies them to problems in QED, advancing understanding of finite-temperature field theories.

Findings

Calculated screening mass squared in Yukawa theory to two-loop order

Computed free energy in Yukawa theory to three-loop order

Compared different approaches to effective field theory construction

Abstract

Chapter one is devoted to a study of fermions and bosons in two spatial dimensions in external electromagnetic fields. The effectve action is calculated by integrating out the matter fields. In chapter two, I investigate the resummation program of Braaten and Pisarski. I calculate the screening mass squared and the free energy in Yukwava theory to two and three-loop order, respectively, in resummed perturbation theory. The main part of the present work is on effective field theories at finite temperature. I discuss the concepts of dimensional reduction, modern renormalization theory, and renormalizable field theories (``fundamental theories'') versus non-renormalizable theories (``effective theories''). Two methods for constructing effective three dimensional field theories are discussed. The first is based on the effective potential, and is applied to field theory with $N$ charged U(N) symmetric scalar coupled to an Abelian gauge field. The second method is an effective field theory approach based on diagrammatical methods, recently developed by Braaten and Nieto. I apply the methods to various problems in spinor and scalar QED.