Zeta-Function Regularization and Scale and Conformal Anomalies for the Landau Problem

Abstract

The technique of ζ-function regularization is used to calculate the anomalies associated with the transformations (t→ e-ρt) and (1/t → 1/t - a) for the Landau Lagrangian. The proper-time transformation function Kij(t,τ;t′,0) now needs to be evaluated exactly, thereby leading to an exact ζ(s,t) for the Landau problem. As a generalization, the calculation when extended to the non-relativistic |ϕ|4 theory in 2+1 dimensions leads to difficulties. We shall discuss some of the difficulties in detail.