Question about SU(n) groups.

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In summary, the conversation discusses the possibility of finding a general method for constructing the generators of a SU(n) group. It is suggested that the method of highest weights can be used to find representations of compact semisimple Lie groups, which is why quantum numbers are discrete. The conversation also touches on the mathematical model needed to represent cooper pairing in superconductors, including the use of spin and spin pairing models. The question of whether a relativistic model is necessary is also raised.
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BlackBaron
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Is there any general method to construct the generators of a SU(n) group?
 
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Originally posted by BlackBaron
Is there any general method to construct the generators of a SU(n) group?

what do you mean "construct"? do you mean "find representation of"? if so, then the answer is "yes!": you can find all the reps of the compact semisimple Lie groups using the method of highest weights. any compact Lie group has a discrete set of representations, which of course is why quantum numbers are quantum, instead of continuous.
 
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Can you tell me what mathematical model you would use to represent cooper pairing in superconductors? I.e. you need a model of spin, and you need a model of spin pairing. What physical model/lie group configuration can explain this? Does it need to be relativistic?

-Mark
 

1. What is an SU(n) group?

An SU(n) group, also known as a special unitary group, is a mathematical group that consists of all n-by-n unitary matrices with determinant equal to 1.

2. What is the significance of SU(n) groups in mathematics?

SU(n) groups are important in mathematics because they are used to study symmetry and transformations in various fields, such as physics, chemistry, and computer science.

3. How are SU(n) groups different from other types of groups?

SU(n) groups are special in that they are both unitary and have a determinant of 1, which means they preserve length and volume in transformations. This makes them useful for studying physical systems.

4. Can you provide an example of an SU(n) group?

An example of an SU(2) group is the group of 2-by-2 unitary matrices with determinant 1, such as [[eiθ, 0],[0, e-iθ]], where θ is a real number.

5. How are SU(n) groups used in physics?

SU(n) groups are used in physics to study symmetries and transformations of physical systems. For example, in quantum mechanics, SU(2) groups are used to describe the symmetries of spin systems.

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