Calculation of Re+e-(s) in (1+1)-dimensional QED: Application of Lanczos tridiagonalization and recursion

A nonperturbative technique for the calculation of the cross section for hadron production in electron-positron annihilation is considered. It is a combination of Lanczos tridiagonalization and recursion used previously by others for calculations of local densities of states that arise in condensed-matter physics. The primary advantage of the technique is that computation of the full spectrum is not required; this can reduce the computing time significantly. The steps by which the approach can be applied to hadron-production calculations are explored. As an illustration, the method is applied to a model process in 1+1 dimensions; however, the approach could be used for (3+1)-dimensional processes, including those governed by quantum chromodynamics.