Lorentz contraction of the equal-time Bethe-Salpeter amplitude in two-dimensional massless quantum electrodynamics

TL;DR

This paper investigates how the equal-time Bethe-Salpeter amplitude in the two-dimensional massless QED (Schwinger Model) approximately exhibits Lorentz contraction when boosted, especially at large quark separations, emphasizing the role of instanton contributions.

Contribution

It demonstrates that the Bethe-Salpeter amplitude shows approximate Lorentz contraction in the Schwinger Model, highlighting the importance of instanton effects for this phenomenon.

Findings

Amplitude exhibits approximate Lorentz contraction at large separations.

Instanton contributions are essential for the Lorentz contraction effect.

Separate topological sectors do not show this property.

Abstract

The Lorentz transformation properties of the equal-time bound-state Bethe-Salpeter amplitude in the two-dimensional massless quantum electrodynamics (the so called Schwinger Model) are considered. It is shown that while boosting a bound state (a `meson') this amplitude is subject to approximate Lorentz contraction. The effect is exact for large separations of constituent particles (`quarks'), while for small distances the deviation is more significant. For this phenomenon to appear, the full} function, i.e. with the inclusion of all instanton contributions has to be considered. The amplitude in each separate topological sector does not exhibit such properties.