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

TL;DR

This paper proposes a modified S-matrix definition to reduce divergences from self-energy contributions, verified through perturbation theory examples, applicable when Hamiltonian operators are known.

Contribution

It introduces a new S-matrix formulation that mitigates self-energy divergences, applicable generally with known Hamiltonian operators.

Findings

Divergences are milder with the new definition.

Verification through perturbation theory examples.

Applicable when total and free Hamiltonians are known.

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.