Compactification near and on the light front

TL;DR

This paper clarifies the relationships among different approaches to compactification near the light front in scalar field theory, demonstrating that zero-mode effects decouple in the continuum limit and covariant results are recovered.

Contribution

It provides a detailed comparison of three quantization methods near the light front and shows that zero-mode induced interactions vanish in the continuum limit, ensuring consistency.

Findings

Zero modes differ between space-like and light front quantization.

Zero-mode induced interactions decouple in the continuum limit.

Compactification on a light-like surface yields a consistent field theory.

Abstract

We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasize the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known ``zero-mode induced'' interaction terms. However, we show that they decouple in the continuum limit and covariant answers are reproduced. Thus compactification of a light-like surface is feasible and defines a consistent field theory.