Light-Front Coupled-Cluster Method In Phi-Four Field Theory

Abstract

The light-front coupled-cluster (LFCC) method is investigated as an alternative method for determining mass eigenvalues in quantum field theories. Traditional methods create an infinite set of coupled equations, and solutions are then approximated by truncating the system of equations and computationally determining the wavefunctions. Instead, the use of an exponential operator to construct the basis set of Fock states allows for generatingthefullsetofstates,maintainingnormalization,whilestillbeingabletocreate a finite problem for the wavefunctions. Application of the LFCC method to phi-4 field theoryisshowntoproducesolutionsingoodagreementwithothermethods. Inparticular, we obtain the masses of the lowest eigenstate as a function of the coupling strength and study the behavior of the wavefunction components. The calculation was facilitated by the construction of a new type of fully symmetric multivariate polynomials used as basis functions for the numerical solution of the LFCC equations. The approximations made for the purpose of this investigation prevented the full scope of symmetry breaking from being observed, but the foundation has been established for future work to apply the LFCC method to symmetry breaking in phi-4 field theory.