Unitarization of symplectics and stability for causal differential equations in Hilbert space

DOI10.1016/0022-1236(81)90078-1zbMath0473.58013OpenAlexW2040444533MaRDI QIDQ1158675

Stephen M. Paneitz

Publication date: 1981

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(81)90078-1

zbMATH Keywords

Cayley transformfield quantizationcausality in groupsinfinite-dimensional symplectic groupsKrein stability theoryspectral properties of linear symplectic operators on a Hilbert spacestability criteria for linear infinite-dimensional Hamiltonian differential equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and semigroups of linear operators (47D03) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Linear differential equations in abstract spaces (34G10) Geometric quantization (53D50) Convex sets and cones of operators (47L07) Stability theory for ordinary differential equations (34D99)

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Dark energy states from quantization of boson fields in a universe with unstable modes, Invariant convex cones and causality in semisimple Lie algebras and groups, Essential unitarization of symplectics and applications to field quantization, Parametrization of causal actions of universal covering groups and global hyperbolicity

Cites Work

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• On the connection between the distribution of poles and residues for an \(R\) function and its invariant derivative
• Quantization of wave equations and hermitian structures in partial differential varieties