Dolan, Brian P. and Nash, Charles
(1992)
Zeta function continuation and the Casimir energy on odd- and even-dimensional spheres.
Communications in Mathematical Physics, 148 (1).
pp. 139-153.
ISSN 1432-0916
Abstract
The zeta function continuation method is applied to compute the
Casimir energy on spheres SN. Both odd and even dimensional spheres are studied.
For the appropriate conformally modified Laplacian A the Casimir energy $ is
shown to be finite for all dimensions even though, generically, it should diverge in
odd dimensions due to the presence of a pole in the associated zeta function ζA(s).
The residue of this pole is computed and shown to vanish in our case. An explicit
analytic continuation of ζA(s) is constructed for all values of N. This enables us to
calculate $ exactly and we find that the Casimir energy vanishes in all even
dimensions. For odd dimensions δ is never zero but alternates in sign as N increases
through odd values. Some results are also derived for the Casimir energy of
other operators of Laplacian type.
| Item Type: |
Article
|
| Additional Information: |
Cite as: Dolan, Brian P.; Nash, Charles. Zeta function continuation and the Casimir energy on odd- and even-dimensional spheres. Comm. Math. Phys. 148 (1992), no. 1, 139--153. https://projecteuclid.org/euclid.cmp/1104250851 |
| Academic Unit: |
Faculty of Science and Engineering > Mathematical Physics |
| Item ID: |
10513 |
| Depositing User: |
Dr. Brian Dolan
|
| Date Deposited: |
19 Feb 2019 17:22 |
| Journal or Publication Title: |
Communications in Mathematical Physics |
| Publisher: |
Springer |
| Refereed: |
Yes |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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