The Heisenberg Matrix Formulation of Quantum Field Theory

TL;DR

This paper extends Heisenberg's matrix formulation to relativistic quantum systems using light-front quantization, enabling the calculation of bound states, scattering processes, and structure functions with frame-independent methods.

Contribution

It introduces discretized light-cone quantization (DLCQ) for relativistic systems, preserving frame independence and enabling matrix diagonalization of the light-front Hamiltonian.

Findings

DLCQ allows calculation of hadron spectra and wavefunctions.

Light-front quantization simplifies boost properties of the partition function.

Final-state rescattering affects structure functions, modifying their relation to wavefunctions.

Abstract

Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time tau = t+z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be obtained from matrix diagonalization of the light-front Hamiltonian on a finite dimensional light-front Fock basis defined using periodic boundary conditions in the light-front space coordinates. This method, discretized light-cone quantization (DLCQ), preserves the frame-independence of the front form even at finite resolution and particle number. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-front partition function, summed over exponentially-weighted light-front energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-front wavefunctions.