Why is the term $m\delta_2\delta_m\bar{\psi}\psi$ ignored in the QED Lagrangian?
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L=ψ¯0(iγμ∂μ−e0γμA0μ−m0)ψ0−14(∂μA0ν−∂νA0μ)2L=ψ¯0(iγμ∂μ−e0γμA0μ−m0)ψ0−14(∂μA0ν−∂νA0μ)2
where the 0 subscript denotes bare fields. The bare fields are related with the renormalized fields via
ψ0=Z2−−√ψA0μ=Z3−−√Aμψ0=Z2ψA0μ=Z3Aμ
m0=Zmme0=Zeem0=Zmme0=Zee
with these redefinitions the Lagrangian takes the form
L=Z2ψ¯iγμ∂μψ−eZeZ2Z3−−√ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2L=Z2ψ¯iγμ∂μψ−eZeZ2Z3ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2
it is customary to define
Z1≡ZeZ2Z3−−√Z1≡ZeZ2Z3
leaving
L=Z2ψ¯iγμ∂μψ−eZ1ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2.L=Z2ψ¯iγμ∂μψ−eZ1ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2.
Moreover, the ZZ renormalization constants are defined to be
Z1=1+δ1Z2=1+δ2Z3=1+δ3Zm=1+δ
where the 0 subscript denotes bare fields. The bare fields are related with the renormalized fields via
ψ0=Z2−−√ψA0μ=Z3−−√Aμψ0=Z2ψA0μ=Z3Aμ
m0=Zmme0=Zeem0=Zmme0=Zee
with these redefinitions the Lagrangian takes the form
L=Z2ψ¯iγμ∂μψ−eZeZ2Z3−−√ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2L=Z2ψ¯iγμ∂μψ−eZeZ2Z3ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2
it is customary to define
Z1≡ZeZ2Z3−−√Z1≡ZeZ2Z3
leaving
L=Z2ψ¯iγμ∂μψ−eZ1ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2.L=Z2ψ¯iγμ∂μψ−eZ1ψ¯γμAμψ−mZ2Zmψ¯ψ−14Z3(∂μAν−∂νAμ)2.
Moreover, the ZZ renormalization constants are defined to be
Z1=1+δ1Z2=1+δ2Z3=1+δ3Zm=1+δ
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Explanation:
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Missing: Remotely
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