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

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Discussion Overview

The discussion revolves around the reasons for the selection of the SU(3), SU(2), and U(1) groups in the Standard Model of particle physics. Participants explore theoretical, historical, and mathematical motivations for these choices without reaching definitive conclusions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about the specific features of SU(3), SU(2), and U(1) that justify their use in the Standard Model.
  • Another participant suggests that the question is fundamentally philosophical, likening it to asking why the laws of nature are as they are, indicating that no definitive answer exists.
  • It is mentioned that the predictions derived from these groups align with experimental observations, though this does not address the underlying reasons for their selection.
  • A summary points out that these groups are used under symmetry to confirm the invariance of certain quantities, but does not elaborate on the implications of this statement.
  • A reference is made to another thread for historical and mathematical motivations, suggesting that further exploration may yield insights.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasons for the selection of these groups, and multiple competing views remain regarding the philosophical and empirical justifications.

Contextual Notes

The discussion highlights limitations in understanding the foundational reasons for the choice of these groups, as well as the dependence on broader philosophical questions about the nature of physical laws.

wasi-uz-zaman
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TL;DR
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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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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Because the predictions that come out match observations.
 
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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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