A note on discrete light cone quantization

TL;DR

This paper examines the validity of discrete light cone quantization (DLCQ) in modeling quark-antiquark bound states in 1+1 dimensions, comparing conditions for reliability with those for black holes in matrix theory.

Contribution

It analyzes the conditions under which DLCQ provides reliable approximations for bound states, linking them to criteria used in black hole matrix theory.

Findings

DLCQ reliability depends on system size and mass.

Conditions for trustworthy DLCQ estimates match those for black holes in matrix theory.

Provides a simple model analogy for understanding DLCQ validity.

Abstract

In this brief note we would like to discuss, in a simple model system, the conditions under which the discrete light cone quantization framework should be trusted as an approximation scheme, with regard, in particular, to the size and mass of the system. Specifically, we are going to discuss ``quark-antiquark'' bound states in 1+1 dim., for which a natural size is provided by analogy with a ``two points and a spring'' system, and show that the condition for obtaining a reliable estimate is the same as the one derived in a recent paper for black holes in matrix theory.