Zabadal, J., Borges, V., Santos, M. and Ribeiro, V. (2015) Analytical Solutions for Dirac and Klein-Gordon Equations Using Bäcklund Transformations—ENFIR 2015 (National meeting of Nuclear Reactor Physics)—Rio de Janeiro, Brasil.

has been cited by the following article:

• TITLE: Fundamental Connections in Differential Geometry: Quantum Field Theory, Electromagnetism, Chemistry and Fluid Mechanics

  AUTHORS: Jorge Zabadal, Ederson Staudt, Ádnei Marinho, Vinícius Ribeiro

  KEYWORDS: Commutation Relations, Extended Navier-Stokes Equations, Extended Helmholtz Equations, Interaction Terms, Quantum Behavior

  JOURNAL NAME: Open Access Library Journal, Vol.10 No.9, September 7, 2023

  ABSTRACT: This work presents novel hydrodynamic formulations that reconcile the continuum hypothesis with the emergence of electromagnetic interactions among molecules from fundamental principles. Two models are proposed: a relativistic version of the Navier-Stokes equations derived from commutation relations, and a Helmholtz-like system obtained by applying the Hodge operator to the extended Navier-Stokes equations. Preliminary analysis suggests that the second model, with its nonlinear terms serving as a generalized current, can reproduce microscopic quantum effects. It shows promise for generating self-consistent field equations via B?cklund transformations, remaining valid across all scales despite the breakdown of the continuum hypothesis.