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.