Fundamental connections in differential geometry : quantum field theory, electromagnetism, chemistry and fluid mechanics

• Autor(a) principal: Zabadal, Jorge Rodolfo Silva
• Data de Publicação: 2023
• Outros Autores: Staudt, Ederson, Marinho, Ádnei, Ribeiro, Vinicius Gadis, Schramm, Marcelo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/264426
• topic: Geometria diferencial; Teoria quantica de campos; Eletromagnetismo; Commutation relations; Extended Navier-Stokes equations; Extended Helmholtz equations; Interaction terms; Quantum behavior

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 Bäcklund transformations, remaining valid across all scales despite the breakdown of the continuum hypothesis.