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absorption operators Action Principle amplitude anticommuting Born approximation Bremsstrahlung calculation commutation laws commutation rules component constant coordinate covariant cross-section defined density Dirac equation Dirac theory divergent effect eigenvalues electrons and positrons emission emitted equation of motion expectation value external potential factor Feynman field equations field operators field theory finite formula free electron free particles frequency function given gives graphs h-vector Hamiltonian Hence initial and final integral interaction representation invariant Lagrangian Lamb shift line-shift Lorentz magnetic matrix element Maxwell field method momentum p energy non-covariant non-relativistic normal constituents observed one-electron pair perturbation theory photon Phys physical polarization positron probability amplitude probability per unit problem quantized quantum electrodynamics quantum theory radiation interaction radiative corrections relativistic quantum theory renormalization result satisfies Schwinger solutions space-like space-time spin spin-states spinor Suppose tion transformation vacuum vacuum expectation value vacuum polarization variation vector wave-function write zero