FEYNMAN'S OPERATIONAL CALCULI FOR NONCOMMUTING OPERATORS: SPECTRAL THEORY

DOI10.1142/S021902570200078XzbMath1096.47502OpenAlexW2057102823MaRDI QIDQ4818892

Gerald W. Johnson, Brian R. F. Jefferies

Publication date: 24 September 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021902570200078x

zbMATH Keywords

joint spectral radiusjoint spectrumfunctional calculus\(n\)-tuples of linear operators

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Functional calculus for linear operators (47A60) Path integrals in quantum mechanics (81S40) Applications of functional analysis in quantum physics (46N50) Spectral sets of linear operators (47A25) Functional calculus in topological algebras (46H30)

Related Items (16)

Feynman's operational calculus with arbitrary measures: an evolution equation in the general case and examples ⋮ Measure decomposing disentangling in Feynman's operational calculus ⋮ Weak convergence and vector-valued functions: Improving the stability theory of Feynman's operational calculi ⋮ Weak convergence and Banach space-valued functions: improving the stability theory of Feynman's operational calculi ⋮ Feynman's operational calculi: Methods for iterative disentangling ⋮ Applications of the monogenic functional calculus for noncommuting systems of operators ⋮ Feynman's operational calculi for noncommuting operators: The monogenic calculus ⋮ Combining continuous and discrete phenomena for Feynman's operational calculus in the presence of a \((C_0)\) semigroup and Feynman-Kac formulas with Lebesgue-Stieltjes measures ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time-dependent setting ⋮ Feynman's operational calculi: decomposing disentanglings ⋮ Feynman's operational calculi: Disentangling away from the origin ⋮ The Weyl correspondence as a functional calculus for non-commuting operators ⋮ Feynman's operational calculi: spectral theory for noncommuting self-adjoint operators ⋮ Stability properties for Feynman's operational calculus in the combined continuous/discrete setting ⋮ Time dependent stability for Feynman's operational calculus ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time independent setting

Cites Work

• The Weyl calculus and commutativity for systems of selfadjoint matrices
• Non-analytic functional calculi in several variables
• Feynman's operational calculus for families of noncommuting operators: tensor products, ordered supports, and the disentangling of an exponential factor
• The Weyl calculus, joint spectra and commutativity of compact selfadjoint operators
• The Weyl functional calculus
• Exponential bounds for noncommuting systems of matrices
• On joint spectra of non-commuting normal operators
• Joint spectra and commutativity of systems of (2 × 2) selfadjoint matrices
• Commutativity of (2 × 2) selfadjoint matrices
• The Weyl functional calculus and two-by-two selfadjoint matrices
• Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
• An Operator Calculus Having Applications in Quantum Electrodynamics

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