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Functional determinants on spheres and sectors
J. S. Dowker
The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of ). The wholesphere and hemis…
Functional determinants on regions of the plane and sphere
J. S. Dowker
The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functio…
A note on Polyakov's nonlocal form of the effective action
J. S. Dowker
A technical point regarding the invariance of Polyakov's nonlocal form of the effective action under uniform rescalings is briefly addressed.
A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope
J. S. Dowker
A derivation of the Cesàro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coe…
Effective action in spherical domains
J. S. Dowker
The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes zeta-functions and it is s…