Yes, Quantum Field Theory can be explained through Lie groups. SU(2) is isomorphic to the quaternions of norm 1, and SU(2) is important if you want to understand the Lorentz group and Poincare group, which represent the symmetries of spacetime and special relativity. Check out the text book Physics From Symmetry by Jakob Schwichtenberg if you would like an approach that derives modern physics primarily from algebra