Zeta-Functions for Non-Minimal Operators

Details Zeta-Functions for Non-Minimal Operators Zeta-Functions for Non-Minimal Operators

1995-03-27

arxiv.org/abs/hep-th/9503188v2

Phys.Rev. D52 (1995) 4588-4599

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, additional references

Scientific paper

10.1103/PhysRevD.52.4588

We evaluate zeta-functions $\zeta(s)$ at $s=0$ for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate $\zeta(0)$ for the cases of Euclidean spaces and $N$-spheres. In the $N$-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting $\zeta(0)$ values for dimensions 2 to 10 are given in the Appendix.

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