Except maybe the math of statistical physics, Lie groups are important everywhere in physics. I used to say mechanics and field(classical and quantum) theory is applied representation theory of a view Lie groups
>>7794500 there are even specific entries, such as https://en.wikipedia.org/wiki/Particle_physics_and_representation_theory
Any Unitary matrix can be written as the matrix exponential of i times a hermitian matrix. This guarantees we can write any transformation of the SU(n) symmetry group in a way that can be: (1) expanded and used in a perturbative theory; (2) related to a physical observable through the postulates of QM. Also, the fundamental representation of the matrix Lie Groups are actually really easy to derive.
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