Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group

DOI10.1063/1.523819zbMath0383.35037OpenAlexW2044951121WikidataQ115332841 ScholiaQ115332841MaRDI QIDQ4163849

Willard jun. Miller, Ernest G. Kalnins

Publication date: 1978

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.523819

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Applications of Lie groups to the sciences; explicit representations (22E70) Partial differential equations of mathematical physics and other areas of application (35Q99) Second-order hyperbolic equations (35L10)

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Identities on solutions of the wave equation in the enveloping algebra of the conformal group ⋮ The wave equation and separation of variables on the complex sphere \(S_ 4\). ⋮ Superintegrable relativistic systems in scalar background fields ⋮ Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry ⋮ Lie theory and the wave equation in space–time. 5. R-separable solutions of the wave equation ψt t−Δ3ψ=0 ⋮ From conformal group to symmetries of hypergeometric type equations ⋮ The Lie Theory of Two-Variable Hypergeometric Functions

Cites Work

• Separable systems of Stäckel
• Symmetry and separation of variables for the Helmholtz and Laplace equations
• Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψt t−Δ2ψ=0
• Lie theory and the wave equation in space–time. I. The Lorentz group
• Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates
• Zur Darstellungstheorie der inhomogenen Lorentzgruppe als Grundlage quantenmechanischer Kinematik