Vejleder: Thomas Ryttov
Projektbeskrivelse
A system has an anomaly when it exhibits a symmetry at the classical level that is broken at the quantum level. In other words when the quantization procedure and quantum fluctuations spoil the symmetry we say that the symmetry is anomalous.
Usually, a first encounter with anomalies happen in quantum field theory when studying the axial and scale anomalies. But in later years it has become clear that anomalies also appear in more simple quantum mechanical systems and hence furnish an excellent introduction to this difficult topic.
The project should discuss scale invariance of mechanical systems including the 1/r^2 potential and the electric dipole potential in three spatial dimensions and the Dirac delta function potential in two spatial dimensions. The project should then study the effects and implications of quantizing the theory and discuss regularization, renormalization, divergences and anomalous symmetry-breaking.