Robert Carroll, Boris Konopelchenko
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. Connection of the GWE inducing with conformal immersion is made and varius aspects of the theory are shown to be invariant under the modified Veselov-Novikov hierarchy of flows. The geometry of certain surfaces is shown to be connected with the dynamics of infinite and finite dimensional integrable systems. Connections to Liouville-Beltrami gravity are indicated.
Robert Carroll
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 is a quantization factor for certain classical systems as well as an expression for quantum matter in gravity theories of Weyl-Dirac type. We extract theories and examples from the literature, providing connections and interpretations, and make a few new observations.
Robert Carroll
We indicate some formulas connecting Ricci flow and the Perelman entropy functional to Fisher information, differential entropy, and the quantum potential.
Robert Carroll
A number of formulas are displayed concerning Whitham theory for a simple example of pure N=2 susy YM with gauge group SU(2). In particular this serves to illuminate the role of Lambda and T derivatives and the interaction with prepotentials F based on Seiberg-Witten and Whitham theory.
Robert Carroll
Jan 14, 2004·quant-ph·PDF Various origins of linear and nonlinear Schrodinger equations are discussed in connection with diffusion, hydrodynamics, and fractal structure. The treatment is mainly expository, emphasizing the quantum potential, with a few new observations.
Robert Carroll
It is shown how formulas of the author for general operator transmutation can be adapted to a quantum group context
Robert Carroll
We review a stability approach to quantization by Rusov and Vlasenko and indicate possible comparisons of fluctuations to standard situations involving a quantum potential.
Robert Carroll
It is shown how the fractal paths of scale relativity (following Nottale) can be introduced into a thermodynamical context (following Asadov-Kechkin).
Robert Carroll
Nov 28, 2012·quant-ph·PDF We describe some analogues of quantum potentials arising in fractional or deformed Schroedinger equations.
Robert Carroll
This is a partially survey collection of material on gravity, entropy, and information with some new heuristic results related to the WDW equation.
Robert Carroll
We show a kind of converse to some results of Hall and Reginatto on exact uncertainty related to the Schroedinger and Wheeler-deWitt equations. Some survey material on statistical geometrodynamics is also sketched.
Robert Carroll
We review some material connecting gravity and the quantum potential and provide a few new observations.
Robert Carroll
We show some relations between Ricci flow and quantum theory via Fisher information and the quantum potential.
Robert Carroll
In a finite zone KdV context we show relations between the duality variables of Faraggi-Matone and those involved in Seiberg-Witten type duality.
Robert Carroll
For certain situations relations are indicated between the space-wave function duality of Faraggi-Matone, enhanced dispersionless KdV, and Whitham dynamics for appropriate hyperelliptic Riemann surfaces related to Seiberg-Witten theory. This paper gives refinements of hep-th/9702138 and some new ideas.
Robert Carroll
We collect a number of facts and conjectures concerning Whitham theory and the renormalization group. Some explicit relations and problems are indicated in the context of N=2 susy Yang-Mills.
Robert Carroll
A possible thermalization of Fisher information is suggested for certain situations.
Robert Carroll
Some situations are discussed where subquantum oscillations in momentum arise in connectiion with Fisher information and the quantum potential.
Robert Carroll
We show explicitly how uncertainty can arise in a trajectory representation. Then we show that the formal utilization of the WKB like hierarchy structure of dKdV in the description of (X,psi) duality does not encounter norm constraints.
Robert Carroll
We show how the WDVV equations and the DZM system can be characterized via a background family of functions.