Differential Geometry of Quantum States, Observables and Evolution
arXiv:1903.10465 · doi:10.1007/978-3-030-06122-7_7
Abstract
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.
20 pages, comments are welcome!
References in corpus (5)
- Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
- Geometry of quantum systems: density states and entanglement
- Dynamical aspects in the Quantizer-Dequantizer formalism
- Dynamical Vector Fields on the Manifold of Quantum States
- Differential Calculus on Manifolds with a Boundary. Applications