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

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.