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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.
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The 4-divergence of this current is: = + where ∂ μ is the 4-gradient and μ is an index labeling the spacetime dimension. Then the continuity equation is: ∂ μ J μ = 0 {\displaystyle \partial _{\mu }J^{\mu }=0} in the usual case where there are no sources or sinks, that is, for perfectly conserved quantities like energy or charge.
The axial current resulting from the motion of an axially charged moving particle is formally defined as = ¯, where is the particle field represented by Dirac spinor (since the particle is typically a spin-1/2 fermion) and and are the Dirac gamma matrices.
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 ...
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Partially conserved axial vector current. Add languages. Add links. Article; ... Download as PDF; ... move to sidebar hide. From Wikipedia, the free encyclopedia ...