Galilean Yang-Mills Theory

Understand

We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories.

• Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime.
• We first explicitly work with the $SU(2)$ theory and then generalise to $SU(N)$ for all $N$, systematising our notation and analysis.
• We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz.