Essential unitarization of symplectics and applications to field quantization

DOI10.1016/0022-1236(82)90091-XzbMath0499.47025OpenAlexW1984440296MaRDI QIDQ1171745

Stephen M. Paneitz

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0022-1236(82)90091-x

zbMATH Keywords

quantum field theoryessentially unique weakly and uniformly closed invariant convex conesinvariant vacuum statequantization of linear time-dependent field equationsskew-adjoint extension of a closed semi- bounded and unbounded infinitesimally symplectic operatorsolution space of the covariant Klein-Gordon equationspectral properties of linear symplectic operators in Hilbert space

Mathematics Subject Classification ID

Applications of operator algebras to the sciences (47L90) Quantum field theory on curved space or space-time backgrounds (81T20) Constructive quantum field theory (81T08) Convex sets and cones of operators (47L07) Linear operators on spaces with an indefinite metric (47B50)

Related Items (5)

``Large conformal metrics of prescribed \(Q\)-curvature in the negative case ⋮ Singular limits for the bi-Laplacian operator with exponential nonlinearity in \(\mathbb R^4\) ⋮ Equivalence of helicity and Euclidean self-duality for gauge fields ⋮ Compactness of solutions to some geometric fourth-order equations ⋮ Unnamed Item

Cites Work

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• Propagateurs et commutateurs en relativité générale
• Mathematical characterization of the physical vacuum for a linear Bose- Einstein field
• Invariant convex cones and orderings in Lie groups
• Complex structure and external fields
• Unitarization of symplectics and stability for causal differential equations in Hilbert space
• Invariant convex cones and causality in semisimple Lie algebras and groups
• Symplectic groups and the Klein-Gordon field
• Existence and uniqueness of the vacuum for linear quantized fields
• The invariance of Poincaré's generating function for canonical transformations
• Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space
• Symplectic geometry
• Quantization of wave equations and hermitian structures in partial differential varieties
• Spaces of positive and negative frequency solutions of field equations in curved space–times. II. The massive vector field equations in static space–times
• Field Quantization
• On general boundary problems for elliptic differential equations
• On continuity and smoothness of group actions
• The Mathematics of Second Quantization
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix

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