Gordon identity

The Gordon identity , named after Walter Gordon , is a decomposition of the Dirac current into terms of the spinor transform operator and the momentum . The decomposition is ${\displaystyle \sigma ^{\mu \nu }=[\gamma ^{\mu },\gamma ^{\nu }]}$

${\displaystyle {\bar {\psi }}(p')\gamma ^{\mu }\psi (p)={\bar {\psi }}(p')\left[{\frac {(p'+p)^{\mu }}{2m}}+{\frac {i\sigma ^{\mu \nu }(p'-p)_{\nu }}{2m}}\right]\psi (p)}$

and follows from the property of the spinors to obey the Dirac equation . The Gordon identity is therefore only valid for particles on the mass shell .

The Gordon identity is required in quantum electrodynamics for the definition of form factors of electron-photon scattering and thus for the calculation of the g-factor of the electron, one of the precision tests of quantum electrodynamics.

literature

• Matthew D. Schwartz: Quantum Field Theory and the Standard Model . Cambridge University Press, New York 2014, ISBN 978-1-107-03473-0 .