A nonperturbative coupled-cluster method for quantum field theories

TL;DR

This paper introduces a nonperturbative coupled-cluster approach for solving bound state problems in quantum field theories using light-front coordinates, avoiding Fock-space truncation and enabling calculation of physical observables.

Contribution

It develops a coupled-cluster method for quantum field theories that circumvents traditional Fock-space truncation, providing a new framework for nonperturbative calculations.

Findings

Formulated a coupled-cluster approach in light-front coordinates.

Derived nonlinear integral equations for the approximation.

Enabled calculation of form factors and observables.

Abstract

The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.