ZETA-FUNCTION REGULARIZATION AND SCALE AND CONFORMAL ANOMALIES FOR THE LANDAU PROBLEM

The technique of zeta-function regularization is used to calculate the anomalies associated with the transformations (t --> e(-rho)t) and (1 /t --> 1/t - a) for the Landau Lagrangian. The proper-time transformat ion function K-ij(t, r; t', 0) now needs to be evaluated exactly, ther eby leading to an exact zeta(s, t) for the Landau problem. As a genera lization, the calculation when extended to the non-relativistic \phi\( 4) theory in 2 + 1 dimensions leads to difficulties. We shall discuss some of the difficulties in detail.