Lie theory and separation of variables. 8. Semisubgroup coordinates for ψtt-Δ2ψ=0

E. G. Kalnins; Willard Miller

doi:10.1063/1.522492

Lie theory and separation of variables. 8. Semisubgroup coordinates for ψ_tt-Δ₂ψ=0

E. G. Kalnins, Willard Miller

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Abstract

We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space-time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO(3,2).

Original language	English (US)
Pages (from-to)	2507-2516
Number of pages	10
Journal	Journal of Mathematical Physics
Volume	16
Issue number	12
DOIs	https://doi.org/10.1063/1.522492
State	Published - 1974
Externally published	Yes

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abstract = "We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space-time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO(3,2).",

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AB - We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space-time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO(3,2).

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Lie theory and separation of variables. 8. Semisubgroup coordinates for ψ_tt-Δ₂ψ=0

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