A new approach to the LSZ reduction formula

Understand

Lehmann, Symanzik and Zimmermann (LSZ) proved a theorem showing how to obtain the S-matrix from time-ordered Green functions.

• Their result, the reduction formula, is fundamental to practical calculations of scattering processes.
• A known problem is that the operators that they use to create asymptotic states create much else besides the intended particles for a scattering process.
• In the infinite-time limits appropriate to scattering, the extra contributions only disappear in matrix elements with normalizable states, rather than in the created states themselves, i.e., the infinite-time limits of the LSZ creation operators are weak limits.