Some remarks on the quantum geometry

Subir K. Bose, Binayak Dutta-Roy

The geometric approach to quantum mechanics initiated by Berry's remarkable discovery [Proc. R. Soc. London Ser. A 392, 45 (1984)] of the anholonomy of the phase of the wave function and subsequent developments leading to a recent reformulation of the geometry of quantum evolution by Anandan and Aharonov [Phys. Rev. Lett. 65, 1697 (1990)] is shown to find an explicit and suggestive realization through the coherent-state representation.

E. R. Caianiello, Giuseppe Marmo, GAETANO SCARPETTA

Robert Carroll

We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.

James Fullwood, Vlatko Vedral

In this Letter, we show how Euclidean three-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal correlations which give rise to geometry are independent of the initial state of the qubit, which we show enables an observer to extract geometric data from sequential measurements without the observer having any knowledge of initial conditions. Such results suggest the plausibility that space itself may emerge from quantum temporal correlations, and we formulate a toy model of such a hypothetical phenomenon.

James Thomas Wheeler