Eur. Phys. J. C (2015) 75: 447
https://doi.org/10.1140/epjc/s10052-015-3679-z

Regular Article - Theoretical Physics

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

Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938, Warsaw, Poland

^* e-mail: t.radozycki@uksw.edu.pl

Received: 14 July 2015
Accepted: 15 September 2015
Published online: 24 September 2015

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.