Non-local structure of renormalized Hamiltonian densities on the light-front hyperplane in space-time

TL;DR

This paper explores the non-local structure of renormalized Hamiltonian densities on the light-front in space-time, highlighting how effective particle size influences interaction non-locality and bound state wave functions.

Contribution

It provides a generic example of non-locality in light-front Hamiltonian densities at first-order in the effective coupling, linking it to bound state wave functions.

Findings

Non-locality depends on the scale parameter of effective particles.

Non-local interaction terms are characterized at first-order in coupling.

Relation established between non-locality and bound state wave functions.

Abstract

When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the arbitrary parameter of scale, which characterizes the size of effective particles in terms of the allowed range of virtual energy changes caused by interactions. This article describes a generic example of the non-locality that characterizes light-front interaction Hamiltonian densities of first-order in an effective coupling constant. The same non-locality is also related to a relative motion wave function for a bound state of two particles.