ON THE CURVATURE OF A CERTAIN RIEMANNIAN SPACE OF MATRICES

DOI10.1142/S0219025700000145zbMath1031.53109arXivmath/9909157WikidataQ115245795 ScholiaQ115245795MaRDI QIDQ4430267

Attila Andai, Peter W. Michor, Dénes Petz

Publication date: 28 October 2003

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

Full work available at URL: https://arxiv.org/abs/math/9909157

zbMATH Keywords

curvature tensorpositive definite matricesscalar curvatureBogoliubov-Kubo-Mori inner productfinite quantum systemtrace 1

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99) Global Riemannian geometry, including pinching (53C20)

Related Items

On the curvature of the quantum state space with pull-back metrics, The \(\alpha\)-geometric structures on manifold of positive definite Hermite matrices, Averaging Symmetric Positive-Definite Matrices, Entropy and isoperimetry for linear and non-linear group actions.

Cites Work

• The Bogoliubov inner product in quantum statistics
• THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS
• Geometry of canonical correlation on the state space of a quantum system