Massless, Euclidean Quantum Electrodynamics on the 5-Dimensional Unit Hypersphere

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Abstract
We show that the Feynman rules for vacuum-polarization calculations and the equations of motion in massless, Euclidean quantum electrodynamics can be transcribed, by means of a stereographic mapping, to the surface of the 5-dimensional unit hypersphere. The resulting formalism is closely related to the Feynman rules, which we also develop, for mass-less electrodynamics in the conformally covariant O(5, 1) language. The hyperspherical formulation has a number of apparent advantages over conventional Feynman rules in Euclidean space: It is manifestly infrared-finite, and it may permit the development of approximation methods based on a semiclassical approximation for angular momenta on the hypersphere. The finite-electron-mass, Minkowski-space generalization of our results gives a simple formulation of electrodynamics in (4, 1) de Sitter space.