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A redefinition of the Lagrangian of a multi-particle system in fieldsreformulates the single-particle, kinetic, and fluid equations governing fluidand plasma dynamics as a single set of generalized Maxwell's equations andOhm's law for canonical force-fields. The Lagrangian includes new termsrepresenting the coupling between the motion of particle distributions, betweendistributions and electromagnetic fields, with relativistic contributions. Theformulation shows that the concepts of self-organization and canonical helicitytransport are applicable across single-particle, kinetic, and fluid regimes, atclassical and relativistic scales. The theory gives the basis for comparingcanonical helicity change to energy change in general systems. For example, ina fixed, isolated system subject to non-conservative forces, a species'canonical helicity changes less than total energy only if gradients in densityor distribution function are shallow.

A field theory approach to the evolution of canonical helicity and energy