Non-Relativistic and Relativistic Lagrangian Pairing in Fluid Mechanics Inspired by Quantum Theory
Year: 2025
Type: article
Abstract: The pairing of non-relativistic and relativistic Lagrangians within the context of fluid mechanics, advancing methodologies for constructing Poincare-invariant Lagrangians, is explored. Through leveraging symmetries and Noether’s theorem in an inverse framework, three primary cases are investigated: potential flow, barotropic flow expressed in terms of Clebsch variables, and an extended Clebsch Lagrangian incorporating thermodynamic effects. To ensure physical correctness, the eigenvalue relation of the energy–momentum tensor, together with velocity normalisation, are applied as key criteria. The findings confirm that the relativistic Lagrangians successfully reduce to their non-relativistic counterparts in the limit c→∞. These results demonstrate a systematic approach that enhances the relationship between symmetries and variational formulations, providing the advantage of deriving Lagrangians that unify non-relativistic and relativistic theories.
Source: Symmetry
DOI: 10.3390/sym17030315
Institutions: Durham University, Heilbronn University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4407789960