Dynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> gauged <mml:math xmlns:mm

We investigate the dynamics of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> gauged <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Q</e:mi></e:math>-balls using fully three-dimensional numerical simulations. We consider two different scenarios: first, the classical stability of gauged <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>Q</g:mi></g:math>-balls with respect to generic three-dimensional perturbations, and second, the behavior of gauged <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Q</i:mi></i:math>-balls during head-on and off-axis collisions at relativistic velocities. With regard to stability, we find that there exist gauged <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>Q</k:mi></k:math>-ball configurations which are classically stable in both logarithmic and polynomial scalar field models. With regard to relativistic collisions, we find that the dynamics can depend on many different parameters such as the collision velocity, relative phase, relative charge, and impact parameter of the colliding <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>Q</m:mi></m:math>-balls. Published by the American Physical Society 2024