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

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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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10.1063/1.522492

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

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).",

author = "Kalnins, \{E. G.\} and Willard Miller",

year = "1974",

doi = "10.1063/1.522492",

language = "English (US)",

volume = "16",

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journal = "Journal of Mathematical Physics",

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publisher = "American Institute of Physics",

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T1 - Lie theory and separation of variables. 8. Semisubgroup coordinates for ψtt-Δ2ψ=0

AU - Kalnins, E. G.

AU - Miller, Willard

PY - 1974

Y1 - 1974

N2 - 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).

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).

UR - https://www.scopus.com/pages/publications/36749105750

UR - https://www.scopus.com/pages/publications/36749105750#tab=citedBy

U2 - 10.1063/1.522492

DO - 10.1063/1.522492

M3 - Article

AN - SCOPUS:36749105750

SN - 0022-2488

VL - 16

SP - 2507

EP - 2516

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 12

ER -

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

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