Solve SU(2) Parametrization Problem w/ Westra's PDF

In summary, the SU(2) parametrization problem is a mathematical problem involving finding parameters for the special unitary group SU(2). Westra, a mathematician, developed a method to solve this problem, outlined in his PDF. Solving the SU(2) parametrization problem is important for accurately describing particle behavior in physics and has applications in other areas of mathematics. Challenges include the complexity of the group and satisfying constraints. Real-world applications include quantum computing, particle physics, and astrophysics.
  • #1
yoreh
2
0
I have a trivial mathematical problem with SU(2) parametrization. In www.mat.univie.ac.at/~westra/so3su2.pdf , section 3, there is a sentence starting with "We first assume b = 0 and find then(...)". My question is: doesn't assuming that b = 0 reduce generality of our parametrization? If not, why?
 
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  • #2
What you need to do there is to consider two mutually exclusive possibilities separately. If b≠0, you can use a strategy that involves division by b. If b=0, that strategy doesn't work, but you can finish the problem without it.
 
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1. What is SU(2) parametrization problem?

SU(2) parametrization problem is a mathematical problem that involves finding a set of parameters to describe the elements of the special unitary group SU(2). This group is used in several areas of physics, including quantum mechanics and particle physics.

2. Who is Westra and what is Westra's PDF?

Westra is a mathematician who developed a method for solving the SU(2) parametrization problem. Westra's PDF is a mathematical document that outlines this method and provides step-by-step instructions for solving the problem.

3. Why is solving the SU(2) parametrization problem important?

The SU(2) parametrization problem is important because it allows scientists to accurately describe the behavior of particles in quantum mechanics and particle physics. It also has applications in other areas of mathematics, such as Lie groups and group theory.

4. What are some challenges in solving the SU(2) parametrization problem?

One of the main challenges in solving the SU(2) parametrization problem is the complexity of the group itself. SU(2) has four dimensions, which can make it difficult to visualize and manipulate. Additionally, the problem involves finding a set of parameters that satisfy certain constraints, which can be challenging to do analytically.

5. Are there any applications of the SU(2) parametrization problem in real-world scenarios?

Yes, there are several applications of the SU(2) parametrization problem in real-world scenarios. One example is in the field of quantum computing, where SU(2) is used to describe the behavior of quantum bits or qubits. It is also used in particle physics to describe the behavior of subatomic particles and in astrophysics to study the behavior of celestial bodies.

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