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

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.