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Continuity equation

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Summary

A local conservation equation of the form βˆ‚tρ+βˆ‡β‹…j=0\partial_t\rho+\nabla\cdot\mathbf j=0; in flat relativistic spacetime it is βˆ‚ΞΌjΞΌ=0\partial_\mu j^\mu=0, while on curved spacetime the corresponding form is βˆ‡ΞΌjΞΌ=0\nabla_\mu j^\mu=0.

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Conservation lawContinuity equation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A local conservation law is expressed by a continuity equation for a density and current.

How to interpret this relation type

A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.

Relation sources

Electric four-currentContinuity equation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Electric charge conservation requires βˆ‚ΞΌjΞΌ=0\partial_\mu j^\mu=0, consistently with Maxwell’s equations.

How to interpret this relation type

Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.

Relation sources

Noether currentContinuity equation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

On the equations of motion and with the stated symmetry assumptions, a Noether current obeys a local continuity equation.

How to interpret this relation type

Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.

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No direct relations are authored in this direction.