A Hamiltonian Light-Front Approach to the Calculation of the Physical Spectrum in Quantum Field Theory

TL;DR

This paper introduces a new light-front Hamiltonian approach for calculating the physical spectrum in quantum field theory, emphasizing rapid convergence and systematic derivation of Hamiltonians for complex theories like QCD.

Contribution

The authors develop a systematic, cutoff-based method to derive Hamiltonians in light-front quantum field theory that respect physical principles and enable spectrum calculations.

Findings

Derived recursion relations for Hamiltonians in phi-cubed theory and QCD.

Computed second- and third-order matrix elements in phi-cubed theory.

Calculated the QCD spectrum to second order and compared with lattice results.

Abstract

We develop a new systematic approach to quantum field theory that is designed to lead to physical states that rapidly converge in an expansion in free-particle Fock-space sectors. To make this possible, we use light-front field theory to isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to force its free-state matrix elements to quickly decrease as the difference of the free masses of the states increases. The cutoff violates a number of physical principles of light-front field theory, including Lorentz covariance and gauge covariance. This means that the operators in the Hamiltonian are not required to respect these physical principles. However, by requiring the Hamiltonian to produce cutoff-independent physical quantities and by requiring it to respect the unviolated physical principles of the theory, we are able to derive recursion relations that define the Hamiltonian to all orders in perturbation theory in terms of the fundamental parameters of the field theory. We present two applications of this method. First we work in massless phi-cubed theory in six dimensions. We derive the recursion relations that determine the Hamiltonian and demonstrate how they are used by computing and analyzing some of its second- and third-order matrix elements. Then we apply our method to pure-glue quantum chromodynamics. After deriving the recursion relations for this theory, we use them to calculate to second order the part of the Hamiltonian that is required to compute the spectrum. We diagonalize the Hamiltonian using basis-function expansions for the gluons' color, spin, and momentum degrees of freedom. We analyze our results for the spectrum, compare them to recent lattice results, and discuss the various sources of error in our calculation.