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Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere

Dennis, M.R. (2004) Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere. Journal of Physics A: Mathematical and General, 37, (40), 9487-9500. (doi:10.1088/0305-4470/37/40/011)
http://eprints.soton.ac.uk/29390/

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Official URL: http://dx.doi.org/10.1088/0305.../37/40/011

Abstract

Any eigenfunction of the Laplacian on a sphere is given in terms of a unique set of directions: these are Maxwell's multipoles, their existence and uniqueness being known as Sylvester's theorem. Here, the theorem is proved by realizing the multipoles are pairs of opposite vectors in Majorana's sphere representation of quantum spins. The proof involves a physicist's standard tools of quantum angular momentum algebra, integral kernels and Gaussian integration. Various other proofs are compared, including an alternative using the calculus of spacetime spinors.

Item Type:	Article
ISSN:	0305-4470
Alternative Locations:	http://www.maths.soton.ac.uk/a...7_9487.pdf
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
School or Centre:	School of Mathematics > Applied Mathematics
ID Code:	29390
Deposited By:	SOMM, Import
Deposited On:	11 May 2006

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