Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-04-17
Nucl.Phys. B532 (1998) 407-428
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTex
Scientific paper
10.1016/S0550-3213(98)00442-8
In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to be extremely efficient. Dirac like operators 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 determinant of a product of differential operators is not equal to the product of the corresponding functional determinants. The simplicity of the Hamiltonian operators chosen is aimed at showing that such situation may be quite widespread in mathematical physics. However, the consequences of the existence of the determinant anomaly have often been overlooked.
Cognola Guido
Elizalde Emilio
Zerbini Sergio
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