APPLICATIONS IN PHYSICS OF THE MULTIPLICATIVE ANOMALY FORMULA INVOLVING SOME BASIC DIFFERENTIAL-OPERATORS

In the framework leading to the multiplicative anomaly formula - which is here proven to be valid even in cases of known spectrum but non-co mpact manifold (very important in Physics) - zeta-function regularisat ion techniques are shown to be extremely efficient. Dirac-like operato rs and harmonic oscillators are investigated in detail, in any number of space dimensions. They yield a non-zero anomaly which, on the other hand, can always be expressed by means of a simple analytical formula . These results are used in several physical examples, where the deter minant of a product of differential operators is not equal to the prod uct of the corresponding functional determinants. The simplicity of th e Hamiltonian operators chosen is aimed at showing that such a situati on may be quite widespread in mathematical physics. However, the conse quences of the existence of the determinant anomaly have often been ov erlooked. (C) 1998 Elsevier Science B.V.