Lie Groups

>>7794327
https://en.wikipedia.org/wiki/Lie_group
https://en.wikipedia.org/wiki/Lie_algebra
https://en.wikipedia.org/wiki/Gauge_theory
https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory

l2google

>>7794327
Quantum physics is a lie invented in the 1920's by a group of physicists. This group is called the "Lie Group".

>why they are important to the standard model

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

>>7796286
11/10

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.

You should really study Yang-Mills, OP.

>>7794327
Because of QCD we can build certain "groups" of particles with sameish attributes. This is helpful to make things easier

Besides that

>muh commutators