Zeta function continuation and the Casimir energy on odd and even dimensional spheres. (English) Zbl 0763.58030
With an eye to applications in quantum field theory this paper deals with the evaluation of the Casimir energy on spheres \(S^ N\). The main tool is the zeta function and its well-established analytic properties. In particular the zeta function is explicitly evaluated at \(-1/2\), yielding directly the Casimir energy when the operator involved in defining the zeta function is essentially the Laplacian (modified by the Ricci scalar). It is shown that under certain conditions (vanishing of the trace anomaly) the Casimir energy as well as the entire energy-momentum tensor may be evaluated in this manner.
Reviewer: S.I.Andersson (Göteborg)
MSC:
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
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