Geometry of positive operators and Uhlmann's approach to the geometric phase

DOI10.1016/S0034-4877(01)80044-6zbMath0978.81037OpenAlexW2041800835MaRDI QIDQ5937881

Alejandra L. Maestripieri, Gustavo Corach

Publication date: 4 February 2002

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(01)80044-6

zbMATH Keywords

parallel transportnatural connectionprincipal bundlespace \(\Omega\) of density operators

Mathematics Subject Classification ID

Infinite-dimensional manifolds (58B99) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items

Transition probability (fidelity) and its relatives ⋮ Off-diagonal quantum holonomy along density operators ⋮ Coherent state map quantization in a Hermitian-like setting

Cites Work

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• A gauge field governing parallel transport along mixed states
• On the operator equation \(BX - XA = Q\)
• Parallel transport and ``quantum holonomy along density operators
• Geometric phases and related structures
• Differential geometry on Thompson's components of positive operators
• Differential and metrical structure of positive operators
• Quantum statistical holonomy
• Quantal phase factors accompanying adiabatic changes
• Hilbert’s projective metric and iterated nonlinear maps
• How and Why to Solve the Operator Equation AX −XB = Y
• A class of connections governing parallel transport along density matrices

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