The Relation Between Equal-Time and Light-Front Wave Functions

TL;DR

This paper investigates the connection between equal-time and light-front wave functions, revealing that common methods are only accurate in the non-relativistic limit and establishing a relation through boosting to the infinite momentum frame.

Contribution

It demonstrates the incorrectness of popular prescriptions for relating wave functions and provides a proven relation via boosting to the infinite momentum frame.

Findings

Popular prescriptions are only valid in the non-relativistic limit.

Boosting to infinite momentum frame relates equal-time and light-front wave functions.

A mathematical relation between integrals of the two wave functions is established.

Abstract

The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the non-relativistic limit. The only presently known way to obtain light-front wave functions from rest-frame, instant-form wave functions is to boost the latter wave functions to the infinite momentum frame. Despite this fact, we prove a relation between certain integrals of the equal-time and light-front wave functions.