On rotations in front form dynamics

TL;DR

This paper investigates the rotational invariance of a 3+1 dimensional front-form dynamics model for positronium, demonstrating high preservation of rotational symmetry and analyzing cut-off dependence.

Contribution

It provides an empirical assessment of rotational symmetry in a specific front-form dynamics model for positronium, highlighting its near invariance and cut-off effects.

Findings

Rotational invariance is preserved to a high degree in the model.

The model reproduces the Bohr and hyperfine structure of positronium.

Dependence on the cut-off is identified and quantified.

Abstract

Quantum field theories in front-form dynamics are not manifestly rotationally invariant. We study a model bound-state equation in 3+1 dimensional front-form dynamics, which was shown earlier to reproduce the Bohr and hyperfine structure of positronium. We test this model with regard to its rotational symmetry and find that rotational invariance is preserved to a high degree. Also, we find and quantify the expected dependence on the cut-off.