The pure state space of quantum mechanics as Hermitian symmetric space

DOI10.1016/S0393-0440(01)00031-6zbMath1032.81021arXivquant-ph/0202076OpenAlexW3098120314MaRDI QIDQ1867206

Alessandro Manià, Renzo Cirelli, Mauro Gatti

Publication date: 2 April 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0202076

zbMATH Keywords

superposition principlegeodesicsRiemannian manifoldsquantum states

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Applications of global differential geometry to the sciences (53C80) Geometry and quantization, symplectic methods (81S10) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Geometric quantization (53D50)

Related Items (9)

Geometric representation theory for unitary groups of operator algebras ⋮ Geometry of quantum dynamics in infinite-dimensional Hilbert space ⋮ Noncommutative integrability from classical to quantum mechanics ⋮ The twofold role of observables in classical and quantum kinematics ⋮ Remarks on geometric quantum mechanics ⋮ Is there a Jordan geometry underlying quantum physics? ⋮ ON UNCERTAINTY, BRAIDING AND ENTANGLEMENT IN GEOMETRIC QUANTUM MECHANICS ⋮ Projective completions of Jordan pairs. II: Manifold structures and symmetric spaces ⋮ Classical and quantum integrability of the three-dimensional generalized trapped ion Hamiltonian

Cites Work

• Reconstructing a nonlinear dynamical framework for testing quantum mechanics
• On the nonlinear extension of quantum superposition and uncertainty principles
• The homotopy type of the unitary group of Hilbert space
• Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space
• The orbit space of the action of gauge transformation group on connections
• Normal pure states of the von Neumann algebra of bounded operators as Kahler manifold
• Quantum mechanics as an infinite-dimensional Hamiltonian system with uncertainty structure: Part I
• Quantum mechanics as an infinite-dimensional Hamiltonian system with uncertainty structure: Part II
• A FUNCTIONAL REPRESENTATION FOR NON-COMMUTATIVE C*-ALGEBRAS
• The Intrinsic Parity of Elementary Particles
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The pure state space of quantum mechanics as Hermitian symmetric space