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- R. Carroll
- 1995

The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.

- Robert Carroll
- 1994

Various connections between 2-D gravity and KdV, dKdV, inverse scattering, etc. are established. For KP we show how to extract from the dispersionless limit of the Fay differential identity of Takasaki-Takebe the collection of differential equations for F = log(τ dKP) which play the role of Hirota type equations in the dispersionless theory. In [7] we… (More)

- ROBERT CARROLL
- 2004

This is a basically expository article tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.

- ROBERT CARROLL
- 2004

We survey various origins and expressions for the quantum potential, expanding and extending the treatment given in a previous paper [35].

Basic quantities related to 2-D gravity, such as Polyakov extrinsic action, Nambu-Goto action, geometrical action, and Euler characteristic are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces in R 3. Connection of the GWE inducing with conformal immersion is made and various aspects of the theory are shown to be invariant under the… (More)

- ROBERT CARROLL
- 2008

We show how Ricci flow is related to quantum theory via Fisher information and the quantum potential.

- ROBERT CARROLL
- 2008

A short survey of some material related to conformal general relativity (GR), integrable Weyl geometry, and Dirac-Weyl theory is given which suggests that various actions can be reformulated in terms of the quantum potential. Possible connections to dark matter are also indicated.

- ROBERT CARROLL
- 2008

We show how the quantum potential arises in various ways and trace its connection to quantum fluctuations and Fisher information along with its realization in terms of Weyl curvature. It represents a genuine quantization factor for certain classical systems as well as an expression for quantum matter in gravity theories of Weyl-Dirac type. Many of the facts… (More)

- ROBERT CARROLL
- 2005

We sketch and emphasize here the automatic emergence of a quantum potential Q in e.g. classical WDW type equations upon inserting a (Bohmian) complex wave function ψ = Rexp(iS/). The interpretation of Q in terms of momentum fluctuations via the Fisher information and entropy ideas is discussed along with the essentially forced role of R 2 as a probability… (More)

- ROBERT CARROLL
- 2008

Some situations are discussed where subquantum oscillations in momentum arise in connection with Fisher information and the quantum potential.