HIGHLIGHTS
SUMMARY
Purpose: Noether`s theorem connects symmetry of the Lagrangian to conserved quantities. In QED, for example, the wave function ψ is invariant under the phase transformations ψ → eiα ψ, for which the authors have the conserved current Jµ ≡ J µ ≡ iψγ µ ψ such that ∂µ J µ=0. There is also the global chiral transformation ψ → eiβγ ψ which has a conserved current only in the massless limit, 5 J 5µ ≡ iψγ 5 γ µ ψ such that ∂µ J 5µ=2imψγ 5 ψ. The authors already know that U symmetry is conserved and for massless fermions both vector current and axial current are conserved, ∂ µ Jµ=0 and . . .
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