SU(3), U(1), O(3), etc what are they?

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Discussion Overview

The discussion revolves around the concepts of various Lie Groups, specifically SU(3), U(1), and O(3), and their significance in the context of symmetry in physics. Participants seek clarification on the definitions and implications of these groups, particularly in relation to the Standard Model of particle physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant requests an explanation of the concepts of SU(3), U(1), and O(3), indicating a lack of understanding of their significance.
  • Another participant identifies these groups as examples of "Lie Groups" and provides links for further reading.
  • A different participant describes SU(3) as the "special unitary group of order 3," O(3) as the "orthogonal group of order 3," and offers an interpretation of U(1) as the multiplicative group of certain complex numbers.
  • It is noted that U(1) corresponds to the photon, SU(2) relates to W and Z bosons, and SU(3) is associated with gluons, suggesting their roles in the Standard Model.

Areas of Agreement / Disagreement

The discussion contains multiple perspectives on the definitions and interpretations of the groups, with no consensus reached on the nuances of U(1) and its implications.

Contextual Notes

Some definitions and interpretations may depend on specific mathematical contexts or physical applications, which are not fully explored in the discussion.

cefarix
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I've heard them used before...some sort of symmetry, but I never figured out what it really is. Can someone please explain the concepts to me? thx
 
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SU(3) is the "special unitary group of order 3": 3 by 3 complex matrices with determinant 1

O(3) is the "orthogonal group of order 3": 3 by 3 real matrices with determinant 1 or -1

U(1) is a bit puzzling! I would interpret U(n) as the "unitary group of order 3": n by n complex matrices with determinant 1 or -1. But "1 by 1 matrices" are just numbers. I guess U(1) would be the multiplicative group with members 1, -1, i, and -i!
 
You will here them used to describe different types of standard model features.

U(1) corresponds to photon
SU(2) to W's and Z's
SU(3) to the gluons.
 

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