By W. Dittrich, M. Reuter
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Additional resources for Effective Lagrangians in Quantum Electrodynamics (Lecture Notes in Physics)
_. t. ,_,. - 1~. is valid. ,.. , we must choose the first part of the counter terms in the form C . ' ~ . 43a) so that ~o(p = -m) = O. 43b) valid, by (m+yH). 45) f --~7--(H-~'t- ~-t-CM÷~)~" We observe appears, that for M ÷ m the well-known which has its origin infrared in the masslessness divergence of the photon. 53 As an important application to the renormalization of the 2-1oop effective are now going to explicitly where ~nr denotes without of the mass operator with regard evaluate the unrenormalized counter terms.
1) as bare wave to fields ~ , ~ which electron propagator or not; the residue is not, however, us to interpret of the electron wave give us a pole one. , up to this order, neglected. C(~) can be If we compare the last expression with the original equation for the unrenormalized electron propagator G~(p) = (~ + m o + Z(~)) -I, we conclude that in the process of renormalization, the bare mass m o has been replaced by the physical mass m and the function C(@) has taken the place of the unrenormalized mass operator Z (2) where C agrees with I (2) from the quadratic term in (@+m) on, but does not contain constant linear terms.
Iteration of Z then gives t I G+ = w h e r e m° r e p r e s e n t s electron, If the unrenormalized we l i m i t ourselves (bare) now t o the mass o f first order the i n ~, then only the diagram has to be calculated, which, according to the usual Feynman rules, leads to w h e r e we chose t h e Feynman gauge f o r D+pv = g#v D+. The s u p e r s c r i p t second-order entire approximation mass o p e r a t o r the consideration structure of of G~(2)(p). ~. , as the pole of the propagator G+ (2) (p) in the presence of interactions with the photon field.