Dynamics on the Light Cone : Compact versus Continuum Quantization

TL;DR

This paper compares compact light cone quantization (DLCQ) and continuum light cone quantization (CLCQ), showing how DLCQ approaches continuum results with minor non-causal terms, while CLCQ maintains causality and proper renormalization.

Contribution

It demonstrates that DLCQ converges to continuum expressions with small non-causal corrections, and establishes that CLCQ provides standard causal results with consistent IR and UV renormalization.

Findings

DLCQ approaches continuum commutators with marginal non-causal terms of order L^{-3/4}.

CLCQ yields standard causal results with proper IR and UV renormalization.

Zero modes influence the IR divergence handling in DLCQ.

Abstract

Compact canonical quantization on the light cone (DLCQ) is examined in the limit of infinite periodicity lenth L. Pauli Jordan commutators are found to approach continuum expressions with marginal non causal terms of order $L^{-3/4}$ traced back to the handling of IR divergence through the elimination of zero modes. In contrast direct quantization in the continuum (CLCQ) in terms of field operators valued distributions is shown to provide the standard causal result while at the same time ensuring consistent IR and UV renormalization.