Remarks on the WDW equation
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.
gr-qc↗
arXiv subjects
Robert Carroll
Publications and source records attributed to Robert Carroll.
Entropy, geometry, and the quantum potential
We sketch and emphasize the automatic emergence of a quantum potential Q in e.g. classical WDW type equations upon inserting a (Bohmian) complex wave function. The interpretation of Q in terms of momentum fluctuations via Fisher information and entropy ideas is discussed along with the essentially forced role of the amplitude squared as a probability density. We also review the constructions of Padmanabhan connecting entropy and the Einstein equations.
physics.class-ph↗
Some fundamental aspects of a quantum potential
We show that given a suitable but essentially arbitrary function Q(x,t,h) there are "generalized" quantum theories having Q as a quantum potential.
quant-ph↗
Remarks on photons and the aether
We expand upon some topics reviewed and sketched in a book to appear with more details, embellishments, and some new material of a speculative nature.
physics.class-ph↗
Fluctuations, gravity, and the quantum potential
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.
gr-qc↗
Fisher, Kaehler, Weyl and the quantum potential
Connections between Fisher information, Kaehler geometry of a quantum projective Hilbert space, and the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter are sketched.
quant-ph↗
Gravity and the quantum potential
We review some material connecting gravity and the quantum potential and provide a few new observations.
gr-qc↗
On the quantum potential
We survey various origins and expressions for the quantum potential with some new observations.
quant-ph↗
Remarks on the Schrodinger equation
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.
quant-ph↗
Integrable systems as quantum mechanics
This is a mainly expository sketch showing how some integrable systems (e.g. KP or KdV) can be viewed as quantum mechanical in nature.
quant-ph↗
Uncertainty, trajectories, and duality
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.
quant-ph↗
Toward a canonical qKdV equation
A new construction, with more visible canonical features, of a qKdV equation in a q-Virasoro context is exhibited.
math.QA↗
Remarks on q-Virasoro and qKdV
Some forms of qKdV type equations are indicated which arise from Virasoro considerations.
math.QA↗
Remarks on quantum differential operators
Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey material.
math.QA↗
Remarks on q-calculus and integrability
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
math.QA↗
Discretization, Moyal, and integrability
Connections of KP, qKP, and Moyal type dKP constructions are developed. Some expansion of the Moyal KP procedures of Kemmoku-Saito is given with clarification of the role of spectral variables as a phase space.
math.QA↗
Discretization and Moyal brackets
We give a q-analysis version of a discretization procedure of Kemmoku and Saito leading to an apparently new q-Moyal type bracket.
math.QA↗
Remarks on quantum transmutation
It is shown how formulas of the author for general operator transmutation can be adapted to a quantum group context
math.QA↗