Invariant inner products on spaces of solutions of the Klein–Gordon and Helmholtz equations

DOI10.1063/1.525109zbMath0473.35009OpenAlexW1965884175MaRDI QIDQ3927547

Kurt Bernardo Wolf, Stanly L. Steinberg

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1063/1.525109

zbMATH Keywords

Euclidean-invariant inner productPoincare- invariant inner productpositive-energy solutionssimilarity groups of the Klein-Gordon and Helmholtz equations

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Geometric theory, characteristics, transformations in context of PDEs (35A30) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items (3)

$SU(2)$ -particle sigma model: momentum-space quantization of a particle on the sphere S ³ ⋮ The relativistic coma aberration. II. Helmholtz wave optics ⋮ Nondiffracting accelerating waves: Weber waves and parabolic momentum

Cites Work

• Irreducible unitary representations of the Lorentz group
• Canonical transforms. IV. Hyperbolic transforms: Continuous series of SL(2,R) representations
• Canonical transforms. II. Complex radial transforms
• Canonical transforms. III. Configuration and phase descriptions of quantum systems possessing an s l (2,R) dynamical algebra
• On the new invariance algebras of relativistic equations for massless particles

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