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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.
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 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]
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 ...
Partially conserved axial vector current. Add languages. Add links. Article; ... Download as PDF; ... move to sidebar hide. From Wikipedia, the free encyclopedia ...
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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.
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