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Functional determinants for radial operators

Gerald V. Dunne
(
- Connecticut U.
)
,
Klaus Kirsten
(
- Baylor U.
)

Jul, 2006

21 pages

Published in:

J.Phys.A 39 (2006) 11915-11928

e-Print:

hep-th/0607066 [hep-th]

DOI:

10.1088/0305-4470/39/38/017

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Abstract:

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We use the zeta function formalism, and the results agree with what one would obtain using the angular momentum cutoff method based on radial WKB. The final expression is numerically equal to an alternative expression derived in a Feynman diagrammatic approach, but is considerably simpler.

Note:

21 pages, uses axodraw.sty Subj-class: High Energy Physics - Theory: Mathematical Physics Journal-ref: J. Phys. A. 39, 11915 (2006) DOI: 10.1088/0305-4470/39/38/017

02.30.Gp
02.30.Tb
03.70.+k
05.45.Mt
operator: differential
operator: determinant
regularization: zeta function
analytic properties

References(40)

Figures(0)

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