Proposal to improve the behaviour of self-energy contributions to the S-matrix

Abstract

A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.

Comments: 24 pages, 1 figure; v2: revised version; v3: section 3 improved. Accepted for publication in Central European Journal of Physics; v4: minor text misprints corrected