Feynman's operational calculi for noncommuting operators: definitions and elementary properties

zbMath1186.81082MaRDI QIDQ873976

Gerald W. Johnson, Brian R. F. Jefferies

Publication date: 3 April 2007

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

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Functional calculus for linear operators (47A60) Path integrals in quantum mechanics (81S40)

Related Items (20)

Effects of absolute continuity in Feynman’s operational calculus ⋮ Feynman's operational calculus with arbitrary measures: an evolution equation in the general case and examples ⋮ The Feynman integral and Feynman's operational calculus: A heuristic and mathematical introduction ⋮ Harmonic Analysis and Stochastic Partial Differential Equations: The Stochastic Functional Calculus ⋮ Two approaches to the use of unbounded operators in Feynman's operational calculus ⋮ 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 ⋮ 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 ⋮ Measure permutation formulas in Feynman's operational calculi ⋮ Feynman's operational calculi: decomposing disentanglings ⋮ Feynman's operational calculi: Disentangling away from the origin ⋮ Feynman's operational calculi: spectral theory for noncommuting self-adjoint operators ⋮ Stability properties for Feynman's operational calculus in the combined continuous/discrete setting ⋮ Generalized measure permutation formulas in Feynman's operational calculi ⋮ Time dependent stability for Feynman's operational calculus ⋮ Towards a comprehensive stability theory for Feynman's operational calculus: the time independent setting

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