Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-10-05
Commun.Math.Phys. 237 (2003) 507-532
Physics
High Energy Physics
High Energy Physics - Theory
Minor changes. Two references added. 24 pages, no figures, LaTeX file
Scientific paper
10.1007/s00220-003-0844-2
The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are stressed, as the intrisic ambiguity present in the definition of the associated fermion functional determinant in the massless case and, also, the unavoidable presence (in some situations) of a multiplicative anomaly, that can be conveniently expressed in terms of the noncommutative residue. The ambiguity is here seen to disappear in the massive case, giving rise to a phase of the Dirac determinant - that agrees with very recent calculations appeared in the mathematical literature - and to a multiplicative anomaly - also in agreement with other calculations, in the coinciding situations. After explicit, nontrivial resummation of the mass series expansions involving zeta and eta functions, the results are expressed in terms of quite simple formulas.
Cognola Guido
Elizalde Emilio
Zerbini Sergio
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