Why are SU(3), SU(2) and U(1) groups used in the Standard Model?

In summary, the Standard Model for particle physics is described by three groups: SU and U. These groups are used to confirm invariance of certain quantities under symmetry. However, it is still unknown why these particular groups were chosen to describe the SM and any answer will only lead to further questions. Despite this, the predictions made by these groups have been observed to match with real-world observations.
  • #1
wasi-uz-zaman
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TL;DR Summary
under symmetry SU and U groups are used to confirm invariance of certain quantities.
hi,
i have studied Standard Model for particle physics - at present it is described by three groups -
1650846005864.png

i have studied - these groups but could not establish what particular feature suggest of these group to be used to describe SM.
Thanks
 
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  • #2
These describe the equations of the SM. This question is isomorphic to "why are the laws of nature what they are and not something else". Nobody knows. Further, any answer will lead to the same question: if I told you they were subgroups of SU(5) wouldn't that just beg the question "why SU(5)?"
 
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  • #3
Because the predictions that come out match observations.
 
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  • #4
wasi-uz-zaman said:
Summary:: under symmetry SU and U groups are used to confirm invariance of certain quantities.

hi,
i have studied Standard Model for particle physics - at present it is described by three groups - View attachment 300525
i have studied - these groups but could not establish what particular feature suggest of these group to be used to describe SM.
Thanks
For historical and mathematical motivations, see my posts in
https://www.physicsforums.com/threads/why-su-2-times-u-1-for-the-sm.846099/
 
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Related to Why are SU(3), SU(2) and U(1) groups used in the Standard Model?

What is the significance of SU(3), SU(2), and U(1) groups in the Standard Model?

The Standard Model is a theory that describes the fundamental particles and their interactions. SU(3), SU(2), and U(1) are three of the groups used in this model to describe the strong, weak, and electromagnetic forces, respectively. These groups play a crucial role in understanding the behavior of these forces and their interactions with matter.

Why are these particular groups chosen for the Standard Model?

These groups were chosen based on experimental evidence and mathematical consistency. The strong force is described by SU(3) because it has three "colors" or types of charges. The weak force is described by SU(2) because it has two types of charges. And the electromagnetic force is described by U(1) because it has one type of charge.

How do these groups relate to the particles in the Standard Model?

Each group corresponds to a set of particles in the Standard Model. SU(3) describes the behavior of quarks, which make up protons and neutrons. SU(2) describes the behavior of the W and Z bosons, which are responsible for the weak force. And U(1) describes the behavior of the photon, which mediates the electromagnetic force.

Can other groups be used in the Standard Model?

While SU(3), SU(2), and U(1) are the main groups used in the Standard Model, other groups can also be used to describe different aspects of particle physics. For example, the Higgs boson, which gives particles their mass, is described by the symmetry group SU(2) x U(1). However, these three groups have been the most successful in describing the fundamental forces and particles in the Standard Model.

What is the role of symmetry in these groups?

Symmetry is a fundamental concept in the Standard Model, and these groups are used to describe the symmetries of the universe. The strong, weak, and electromagnetic forces are all described by symmetries, and these groups help us understand how these symmetries manifest in the behavior of particles and forces. Additionally, the Standard Model is based on the principle of gauge symmetry, which is described by these groups.

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