Weight diagrams and Lie algebras

In summary, the conversation discusses the identification of sets of particles with the weights of a semi-simple Lie algebra, such as the baryon octet with the 8 representation of SU(3) global flavour symmetry and the 3 weak bosons with the triplet representation of local SU(2) weak isospin symmetry. The question arises whether a single weight diagram can belong to two semi-simple Lie algebras or if the structure of the weight diagram uniquely determines the associated algebra. The conversation also mentions the consideration of non-trivial cases and the clarification that the weight diagrams correspond to irreducible representations in particle physics.
  • #1
metroplex021
151
0
Very often we've identified sets of particles with the weights of a semi-simple Lie algebra - for example, the 8 particles of the baryon octet with the weights of the 8 representation of SU(3) global flavour symmetry (in the old days of the Eightfold Way), or the 3 weak bosons with the weights of the triplet representation of local SU(2) weak isospin symmetry. Does anybody know if it's possible for a single weight diagram to belong to two semi-simple Lie algebras? Or does the structure of a weight diagram determine the associated algebra uniquely? Any thoughts would be really appreciated.
 
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  • #2
A mathematician immediately thinks of the trivial case -- the singlet representation.
 
  • #3
OK - then let *me* specify non-trivial cases! And - as I should have said before - the weight diagrams in question correspond to *irreducible* representations (since these are what we usually deal with in particle physics anyway). Thanks.
 

1. What are weight diagrams and Lie algebras?

Weight diagrams and Lie algebras are mathematical tools used to study the symmetries of physical systems. They are particularly useful in the field of particle physics and quantum mechanics.

2. How are weight diagrams and Lie algebras related?

Weight diagrams are graphical representations of Lie algebras, which are mathematical structures used to describe symmetries and transformations in a system. The weight diagram provides a visual representation of the algebra's structure and helps to understand its properties.

3. What is the significance of weight diagrams and Lie algebras in physics?

Weight diagrams and Lie algebras are crucial in understanding the symmetries and symmetrical transformations of physical systems. They are used to describe the behavior of subatomic particles, such as quarks and leptons, and are essential in the development of theories in particle physics.

4. How do weight diagrams and Lie algebras help in solving physical problems?

Weight diagrams and Lie algebras provide a systematic and organized way to study the symmetries and transformations in a physical system. They can help in predicting the behavior of particles, identifying different states of a physical system, and solving complex mathematical equations.

5. Are there any real-world applications of weight diagrams and Lie algebras?

Yes, weight diagrams and Lie algebras have numerous practical applications, particularly in particle physics and quantum mechanics. They are also used in fields such as chemistry, crystallography, and even computer science, to study the symmetries and transformations in complex systems.

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