Non-linear conformally invariant generalization of the Poisson equation to D>2 dimensions

Abstract

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that is second order, and in which the scalar $phi$ couples to the sources $\rho$ via a $\varphi \rho$ contact term. The symmetry is used to generate solutions for the field for some non-trivial configurations (e.g. for two oppositely charged points). Systems comprising N point charges afford further application of the symmetry. For these I derive e.g. exact expressions for the following quantities: the general two-point-charge force; the energy function and the forces in any three-body configuration with zero total charge; the few-body force for some special configurations; the virial theorem for an arbitrary, bound, many-particle system relating the time-average kinetic energy to the particle charges. Possible connections with an underlying conformal quantum field theory are mentioned.

Revtex, 16 pages. To be published in Phys. Rev. E

Cited by in corpus (28)

• Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions
• Modified Newtonian Dynamics as an Alternative to Dark Matter
• Quasi-linear formulation of MOND
• Theory of Dark Matter Superfluidity
• A new relativistic theory for Modified Newtonian Dynamics
• Field-theoretical formulations of MOND-like gravity
• The modified Newtonian dynamics-MOND-and its implications for new physics
• MOND theory
• A Nonlocal Metric Formulation of MOND
• MOND laws of galactic dynamics
• The MOND limit from space-time scale invariance
• MOND habitats within the solar system
• Cosmological fluctuation growth in bimetric MOND
• Marriage à-la-MOND: Baryonic dark matter in galaxy clusters and the cooling flow puzzle
• Comparing different realizations of modified Newtonian dynamics: virial theorem and elliptical shells
• Galaxy groups and the modified dynamics
• Electrodynamics a la Horava
• MOND mass-to-light ratios for galaxy groups
• General virial theorem for modified-gravity MOND
• Mond - a review
• Matter and twin matter in bimetric MOND
• Forces in Nonlinear Media
• MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling
• Theoretically motivated dark electromagnetism as the origin of relativistic MOND
• Suspension and levitation in nonlinear theories
• The p-Laplacian as a Framework for Generalizing Newtonian Gravity and MoND
• The Jeans theorem and the "Tolman-Oppenheimer-Volkov equation" in an exact wave solution of R^2 gravity
• Fast particle-mesh code for Milgromian dynamics