Renormalization of the classical massless
scalar field theory with quartic self-interaction.
Faculty of Physics, Ludwig-Maximilians-Universität München.
The classical theory of the massless scalar field with negative quartic selfinteraction shows asymptotic freedom and confinement. These findings might help in understanding evidence, gathered from experiment and lattice simulations of quantum chromodynamics, that quarks can't be found alone. To improve the understanding of these results the renormalization of the classical massless scalar field theory with quartic self-interaction is studied in detail. The renormalized effective coupling is obtained twice, using different regularization schemes: Cutoff regularization and dimensional regularization. The renormalization group is explained. The perturbative expansion of the effective coupling is improved by enforcing the renormalization group law. A connection to renormalization and the renormalization group found in other areas of physics is made.