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## Main Question or Discussion Point

In Peskin and Schroeder at page 323 second paragraph the author state

'To obtain finite results for an amplitude involving divergent diagrams, we have so far used the following procedure: Compute the diagrams using a regulator to obtain an expression that depends on the bare mass (m0), the bare coupling constant (e0) and some UV cutoff ([itex]\Lambda[/itex]). Then compute the physical mass (m) and the physical coupling constant (e), to whatever order is consisten with the rest of the calculation; these quantities will also depend on m0, e0 and [itex]\Lambda[/itex]. To calculate an S-matrix element one must also compute the field-strength renormalization Z (according to the LSZ formula). Combining all of these expression, eliminate m0 and e0 in favour of m and e; this step is the 'renormalization'. The resulting expression for the amplitude should be finite in the limit [itex] \Lambda \to \infty[/itex].'

Where does the author actually use this procedure to compute an S-matrix element?

Have I understood it correctly if the point is that when one inserts the relations m(m0), e(e0) and Z into the LSZ formula the divergences in the respective relations cancel each other out to a given order?

'To obtain finite results for an amplitude involving divergent diagrams, we have so far used the following procedure: Compute the diagrams using a regulator to obtain an expression that depends on the bare mass (m0), the bare coupling constant (e0) and some UV cutoff ([itex]\Lambda[/itex]). Then compute the physical mass (m) and the physical coupling constant (e), to whatever order is consisten with the rest of the calculation; these quantities will also depend on m0, e0 and [itex]\Lambda[/itex]. To calculate an S-matrix element one must also compute the field-strength renormalization Z (according to the LSZ formula). Combining all of these expression, eliminate m0 and e0 in favour of m and e; this step is the 'renormalization'. The resulting expression for the amplitude should be finite in the limit [itex] \Lambda \to \infty[/itex].'

Where does the author actually use this procedure to compute an S-matrix element?

Have I understood it correctly if the point is that when one inserts the relations m(m0), e(e0) and Z into the LSZ formula the divergences in the respective relations cancel each other out to a given order?