Renormalization in Field Theories

by Alexander Söderberg

Institution: Uppsala University
Year: 2015
Keywords: renormalization in field theories; renormalization; quantum field theories; quantum field theory; quantum mechanics; quantum physics; quantum; physics; mechanics; field theory; theory; theories; fields; field; regularization; dimensional regularization; dimensional; perturbative; perturbative renormalization; wilsonian approach; wilsonian; approach; momentum cutoff; momentum; cutoff; callan; symanzik; equation; callan symanzik equation; coleman; weinberg; model; potential; effective; coleman-weinberg potential; beta function; beta; non abelian; gauge; non abelian gauge theory; non abelian gauge theories; qed; quantum electrodynamics; electrodynamics; qcd; quantum chromodynamics; chromodynamics; Natural Sciences; Physical Sciences; Other Physics Topics; Naturvetenskap; Fysik; Annan fysik; Masterprogram i fysik; Master Programme in Physics
Record ID: 1365142
Full text PDF: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-251561


Several different approaches to renormalization are studied. The Callan-Symanzik equation is derived and we study its beta functions. An effective potential for the Coleman-Weinberg model is studied to find that the beta function is positive and that spontaneous symmetry breaking will occur if we expand around the classical field. Lastly we renormalize a non-abelian gaugetheory to find that the beta function in QCD is negative.