M R Dennis 2004 J. Phys. A: Math. Gen. 37 9487 doi:10.1088/0305-4470/37/40/011
Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere
M R Dennis
Show affiliationsAny 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.
- PACS
- MSC
- Subjects
- Dates
-
Issue 40 (8 October 2004)
Received 26 July 2004
Published 22 September 2004
-
Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere
M R Dennis 2004 J. Phys. A: Math. Gen. 37 9487
-
Anisotropy Studies of the Unresolved Far-Infrared Background
Alexandre Amblard and Asantha Cooray 2007 ApJ 670 903
-
Small-Scale Anisotropy of Cosmic Rays above 1019 eV Observed with the Akeno Giant Air Shower Array
M. Takeda et al. 1999 ApJ 522 225
-
Bars and Warps Traced by the Molecular Gas in the Seyfert 2 Galaxy NGC 1068
E. Schinnerer et al. 2000 ApJ 533 850
-
Mean spherical model for two-component plasmas
U De Angelis et al 1980 J. Phys. C: Solid State Phys. 13 3649
-
Effect of nanoparticles on sessile droplet contact angle
S Vafaei et al 2006 Nanotechnology 17 2523
-
A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators
Feng Liu et al 2005 Phys. Med. Biol. 50 5281
-
Waiting-Time Distributions in Lattice Models of Solar Flares
James P. Norman et al. 2001 ApJ 557 891
-
Algebraic nature of shape-invariant and self-similar potentials
A B Balantekin et al 1999 J. Phys. A: Math. Gen. 32 2785
-
Mg–He and Ca–He van der Waals interactions: approaching the Born–Oppenheimer limit
Robert J Hinde 2003 J. Phys. B: At. Mol. Opt. Phys. 36 3119
Users also read
What's this?Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*