Nonperturbative light-front effective potential for static sources in quenched scalar Yukawa theory

TL;DR

This paper calculates a nonperturbative, rotationally symmetric effective potential between static sources in a light-front scalar Yukawa model, matching the Yukawa form despite coordinate symmetry breaking.

Contribution

It introduces a nonperturbative method to derive an effective potential in light-front quantization that preserves rotational symmetry and models scalar interactions with coherent states.

Findings

Effective potential matches standard Yukawa potential.

Rotational symmetry is preserved despite light-front coordinate use.

Eigenstates of the Hamiltonian determine the potential.

Abstract

We compute an effective potential between two fixed sources in light-front quantization of a quenched scalar Yukawa theory that models the interaction of complex scalar fields through the exchange of a neutral scalar. Despite the breaking of explicit rotational symmetry by the use of light-front coordinates, the effective potential is rotationally symmetric and matches the standard Yukawa potential for scalar exchange. The neutral scalar field is represented by a coherent state, which is obtained nonperturbatively as an eigenstate of our model Hamiltonian, with the eigenenergy determining the effective potential. The sources are represented by wave packets that are fixed with respect to ordinary time, but move in light-front coordinates. The theory is quenched, to remove pair-production processes that would otherwise cause the spectrum to be unbounded from below.