Unit:
Department of PhysicsLibrary of the School of Science
Supervisors info:
Νικόλαος Τετράδης, Καθηγητής, Τμήμα Φυσικής, Σχολή Θετικών Επιστημών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Ομάδα Επανακανονικοποίησης και μη Αβελιανές Θεωρίες Βαθμίδας
Translated title:
Renormalisation Group and non Abelian Gauge Theories
Summary:
In the present work we study the renormalization of gauge theories. We begin by extracting the lagrangian of those theories using general symmetry arguments. By demanding that the lagrangian remains invariant under local SU(N) transformations, we arrive at gauge theories called Yang-Mills theories.We move on to quantize those theories. We implement a method developed by Faddeev and Popov, in order to extract only the physical degrees of freedom.
We then derive the Callan-Symanzik renormalization group equation for the renormalized green functions. We define the beta function and then we compute it perturbatively.
Next, we study Quantum Electrodynamics (QED) at one loop level. After canceling the infinities that arise at one loop order, we compute the first quantum corrections to the electromagnetic coupling and the gyromagnetic ratio of the electron.
Finally, we study the one loop structure of a general non Abelian gauge theory, so as to compute its beta function. It turns out that Quantum Chromodynamics (QCD), the SU(3) non abelian theory, is an asymptotically free theory, in contrast to QED, for a given small number of fermions.
Main subject category:
Science
Other subject categories:
Physics (theory)
Keywords:
Renormalisation Group, Gauge Theories, Quantum Field Theory, Quantum Electrodynamics, Quantum Chromodynamics, Yang-Mills Theories
