Is Weak Isospin Conservation Provable Using Noether's Theorem?

In summary, the conversation discusses the possibility of using Noether's theorem to prove that weak isospin associated with SU(2) is conserved. However, it is concluded that this is not possible as weak isospin is not conserved. The conversation also delves into the mathematical demonstration of the association between SU(2) and weak isospin and the understanding of symmetries and group generators. It is revealed that the individual asking the questions has no background in particle physics but is trying to learn from books and videos. The conversation also references a document discussing the topic further.
  • #1
nigelscott
135
4
Is it possible to prove that weak isospin associated with SU(2) is conserved using Noether's theorem?
 
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  • #2
Considering that weak isospin is not conserved, the answer is "no".
 
  • #3
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?
 
  • #5
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.
 

Related to Is Weak Isospin Conservation Provable Using Noether's Theorem?

1. What is Noether's Theorem?

Noether's Theorem is a fundamental concept in mathematical physics that states that for every continuous symmetry in a physical system, there exists a corresponding conserved quantity.

2. What is SU(2)?

SU(2) is a special unitary group in mathematics that is used to describe the symmetries of quantum mechanical systems. It is also an important component in the Standard Model of particle physics.

3. How does Noether's Theorem relate to SU(2)?

Noether's Theorem applies to any continuous symmetry, including the symmetries described by SU(2). This means that for every symmetry in an SU(2) system, there exists a corresponding conserved quantity.

4. What are some applications of Noether's Theorem and SU(2)?

Noether's Theorem and SU(2) have various applications in physics, including in the study of quantum mechanics, particle physics, and general relativity. They are also used in the development of advanced technologies, such as quantum computing.

5. How does Noether's Theorem and SU(2) contribute to our understanding of the universe?

By revealing the connection between symmetries and conserved quantities, Noether's Theorem and SU(2) help us understand the fundamental laws of nature and the underlying symmetries that govern the behavior of the universe. They also play a crucial role in the development of theories and models that describe our world.

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