Is Weak Isospin Conservation Provable Using Noether's Theorem?

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Discussion Overview

The discussion revolves around the possibility of proving weak isospin conservation associated with SU(2) using Noether's theorem. It explores the relationship between symmetries in particle physics and their corresponding conservation laws, particularly focusing on weak isospin and weak hypercharge.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether weak isospin conservation can be proven using Noether's theorem.
  • Another participant asserts that weak isospin is not conserved, suggesting that a proof is not possible.
  • A participant seeks clarification on how to mathematically demonstrate that SU(2) is associated with weak isospin, referencing the established connection between U(1) symmetry and weak hypercharge.
  • Concerns are raised about the understanding of symmetry and its generators in the context of particle physics, questioning the foundational knowledge of the original poster.
  • The original poster acknowledges their lack of background in particle physics but expresses a desire to learn and fill gaps in their understanding of symmetries and group generators.
  • A link to an external document is shared, presumably related to the topic, although the participant notes difficulty in reading it due to formatting.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the conservation of weak isospin, with some asserting it is not conserved while others explore the theoretical implications of Noether's theorem in this context. The discussion remains unresolved with multiple competing views.

Contextual Notes

There are limitations in the discussion regarding the foundational understanding of symmetries and their implications in particle physics, as well as the assumptions underlying the relationship between Noether's theorem and weak isospin.

nigelscott
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Is it possible to prove that weak isospin associated with SU(2) is conserved using Noether's theorem?
 
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Considering that weak isospin is not conserved, the answer is "no".
 
Maybe I asked the question in the wrong way (or maybe not!). It is possible to use Noether's theorem to show that U(1) symmetry is associated with charge (weak hypercharge). So how do you demonstrate mathematically that SU(2) is associated with weak isospin?
 
Certainly not taken the wrong way. I have no background in particle physics. I am a retired electrical engineer with a decent background in QM. I am trying to learn this stuff from books and videos (notably Susskind's videos on the Standard Model). There are lot of gaps that I am trying to fill and more often than not I get things messed up. But that's OK as long I keep learning and don't waste too many people's time . That said, I think I now have a basic understanding of symmetries and group generators. I understand that weak hypercharge is the generator of U(1) and weak isospin is the generator of SU(2). According to Noether, rotational symmetries are associated with charge. I thought there may be a corresponding argument that associates SU(2) with weak isospin.

Re the W boson post. Yes, you are correct about this too. However, responses to this post and others have helped me enormously. In retrospect, I would draw the same conclusion that you did about my level of understanding.
 

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