Quantum analysis -- non-commutative differential and integral calculi

DOI10.1007/BF02506410zbMath0874.46045MaRDI QIDQ1356107

Masuo Suzuki

Publication date: 8 July 1997

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

zbMATH Keywords

inner derivationquantum statistical physicsderivatives of hyperoperatorsnon-commutative calculus of operator derivatives and integrals

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items (13)

Derivation of density operators for generalized entropies with quantum analysis ⋮ GENERAL FORMULATION OF QUANTUM ANALYSIS ⋮ SYNERGISM IN ORDER FORMATION FROM UNSTABLE FLUCTUATIONS ⋮ CORRELATION IDENTITIES AND APPLICATION ⋮ Derivation of the density operator with quantum analysis for the generalized Gibbs ensemble in quantum statistics ⋮ Goldberg's theorem and the Baker-Campbell-Hausdorff formula ⋮ Derivations, derivatives and chain rules ⋮ DUAL GEOMETRY OF THE WIGNER–YANASE–DYSON INFORMATION CONTENT ⋮ Variation of induced linear operators ⋮ Connecting the Kontsevich-Witten and Hodge tau-functions by the \(\widehat{GL(\infty)}\) operators ⋮ Quantum analysis on the convergence speed of exponential product formulas — differential-subtraction and exchange-integration method on concise norm bounds ⋮ COMPUTATIONICS AND QUANTUM ANALYSIS ⋮ COMPUTATIONICS AND QUANTUM ANALYSIS

Cites Work

• Unnamed Item
• Statistical physics II. Nonequilibrium statistical mechanics. Rev. transl. of the rev. orig. Jap. ed.
• Quantum Monte Carlo methods and general decomposition theory of exponential operators and symplectic integrators
• Convergence of general decompositions of exponential operators
• Nonlinear fluctuations, separation of procedures and linearization of processes
• Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics
• Comment on ‘‘Compact expression for Löwdin’s alpha function’’ [J. Math. Phys. 2 6, 940 (1985)]
• General theory of fractal path integrals with applications to many-body theories and statistical physics
• Geometry of canonical correlation on the state space of a quantum system

This page was built for publication: Quantum analysis -- non-commutative differential and integral calculi