On the nonlinear extension of quantum superposition and uncertainty principles

DOI10.1016/S0393-0440(98)00031-XzbMath0939.58005OpenAlexW2050280807MaRDI QIDQ1299126

Mauro Gatti, Renzo Cirelli, Alessandro Manià

Publication date: 11 July 2000

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

Full work available at URL: https://doi.org/10.1016/s0393-0440(98)00031-x

zbMATH Keywords

superposition principlegeodesicsRiemannian manifoldsuncertainty principlequantum mechanicsPoisson algebrasquantum states

Mathematics Subject Classification ID

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Geodesics in global differential geometry (53C22)

Related Items (7)

A geometrical setting for geometric phases on complex Grassmann manifolds ⋮ The twofold role of observables in classical and quantum kinematics ⋮ Remarks on geometric quantum mechanics ⋮ K\"ahler geometry on complex projective spaces via reduction and unfolding ⋮ ON UNCERTAINTY, BRAIDING AND ENTANGLEMENT IN GEOMETRIC QUANTUM MECHANICS ⋮ Differential geometry of density states ⋮ The pure state space of quantum mechanics as Hermitian symmetric space

Cites Work

• Pure states as a dual object for C*-algebras
• Critical point theory and submanifold geometry
• Lusternik-Schnirelman theory on Banach manifolds
• On unitary ray representations of continuous groups
• 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
• Geometry of quantum evolution
• A Superposition Principle in Physics
• Symmetry in Quantum Theory
• The Intrinsic Parity of Elementary Particles
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