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1	Renormalization in Field Theories Söderberg, Alexander January 2015 (has links) 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. 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