International Journal of Theoretical Physics

, Volume 51, Issue 3, pp 667-683

First online:

Hydrodynamics, Particle Relabelling and Relativity

  • Peter HollandAffiliated withGreen Templeton College, University of Oxford Email author 

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Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through Eulerian-picture models that are distinguished by their Lorentz transformation properties. Introducing the idea of the relativity of the particle label, it is demonstrated how the corresponding trajectory models are compatible with the relativity principle. It is also shown how the Eulerian variational formulation may be obtained by canonical transformation from the Lagrangian picture, and how symmetries in the Lagrangian picture may be used to generate Eulerian conserved charges.


Hydrodynamics Lagrangian picture Particle label Relativity Symmetries