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the breaking radiation emitted by the scattering of an electron with an external field is described by the hamiltonian:

[tex]

H=\bar \Psi^- (\displaystyle{\not}{A}_e + \displaystyle{\not}A) \Psi^+

[/tex]

where [itex]A_e[/itex] is the external static classical field, while [itex]A[/itex] is the quantized field.

The breaking radiation at the second order is given by (up to some constants):

[tex]

S^{(2)}=\int d^4 x_1 d^4 x_2 T \{ N [ \bar \Psi^- (\displaystyle{\not}{A}_e + \displaystyle{\not}A) \Psi^+ ]_{x_1} N[\bar \Psi^- (\displaystyle{\not}{A}_e + \displaystyle{\not}A) \Psi^+] _{x_2}\}

[/tex]

where T is the time-ordered product and N is the normal product.

If I contract the two fermion fields (e.g. [itex]\bar \Psi^- (x_1)[/itex] with [itex]\Psi^+ (x_2)[/itex] I get that in both x1 and x2 there is the interaction between an electron, the external field and the quantized field. But in all the feynman diagrams I saw, in x1 there is only the interaction between the electron and the external field, whereas in x2 there is only the interaction between the electron and the quantized field.... how can this be possible?

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# Feynman diagrams for Bremsstrahlung

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