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In physics a conserved current is a current, , that satisfies the continuity equation =.The continuity equation represents a conservation law, hence the name. Indeed, integrating the continuity equation over a volume , large enough to have no net currents through its surface, leads to the conservation law =, where = is the conserved quantity.
Since there is no known massless fermion in nature, chiral symmetry is at best an approximate symmetry in fundamental theories, and the axial current is not conserved. (Note: this explicit breaking of the chiral symmetry by non-zero masses is not to be confused with the spontaneous chiral symmetry breaking that plays a dominant role in hadronic ...
In the one-dimensional space a conservation equation is a first-order quasilinear hyperbolic equation that can be put into the advection form: + = where the dependent variable y(x,t) is called the density of the conserved (scalar) quantity, and a(y) is called the current coefficient, usually corresponding to the partial derivative in the ...
In modern terminology, the conserved quantity is called the Noether charge, while the flow carrying that charge is called the Noether current. The Noether current is defined up to a solenoidal (divergenceless) vector field. In the context of gravitation, Felix Klein's statement of Noether's theorem for action I stipulates for the invariants: [7]
The term on the right is the divergence of the current density J at the same point. The equation equates these two factors, which says that the only way for the charge density at a point to change is for a current of charge to flow into or out of the point. This statement is equivalent to a conservation of four-current.
Current events; Conserved current, a concept in physics and mathematics that satisfies the continuity equation; Current density, a mathematical concept unifying electric current, fluid current, and others; Current River (Ozarks), Missouri, US; Currant (disambiguation) Kurrent, German handwriting style
This is an accepted version of this page This is the latest accepted revision, reviewed on 14 January 2025. Law of physics and chemistry This article is about the law of conservation of energy in physics. For sustainable energy resources, see Energy conservation. Part of a series on Continuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws ...
Conservation form or Eulerian form refers to an arrangement of an equation or system of equations, usually representing a hyperbolic system, that emphasizes that a property represented is conserved, i.e. a type of continuity equation.