- #1
gheremond
- 7
- 0
In QED, the Ward identities set [tex] Z_1=Z_2 [/tex] and [tex] Z_1 - 1 = \left. {\frac{{d\Sigma \left( p \right)}}{{dp}}} \right|_{p = m} [/tex]. This can be shown explicitly for the 1-loop calculations if one uses an on-shell subtraction scheme, where the renormalized mass and charge are identical to the experimentally measured ones. What happens if one uses instead a subtraction scheme like MS or [tex] \overline {MS} [/tex]? Arguably the Ward identities should hold again, but in calculating the various Z functions, one finds that [tex] Z_1 - 1 = \left. {\frac{{d\Sigma \left( p \right)}}{{dp}}} \right|_{p = m} [/tex] only holds at the level of the infinite contributions (poles), while there are some finite differences. Is that supposed to happen? Do the identities only refer to the infinite parts of the renormalization functions?