Lie Groups

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Anonymous

Lie Groups 2016-01-19 00:32:33 Post No. 7794327

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Lie Groups 2016-01-19 00:32:33 Post No. 7794327

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Can anyone explain Lie groups and why they are important to the standard model?

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>>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

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>>7794327

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

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>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

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>>7796286

11/10

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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.

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>>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

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