Zeta-function regularization and scale and conformal anomalies for the Landau problem

The technique of ζ-function regularisation 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.