Invariance of Hamiltonian of strong interaction under SU(6)

In summary, the problem at hand involves showing that if the Hamiltonian of the strong interaction is invariant under SU(6) Spin-Flavor, it is possible to explain the mixing of pseudo scalar and vectorial mesons in the octet and singlet (η − η’ y ω − φ). The student has attempted to find helpful resources, but has not been successful and is seeking assistance in solving the problem.
  • #1
Phys_cruino
2
0
Dear all, this is my first thread in the forum.
I am trying to solve the following problem. it was given during a written exam at my university (many years ago) and I really would appreciate if someone will help me to solve it


1. Homework Statement
Show that if the hamiltonian of the strong interaction is invariant under SU(6) Spin- Flavor (instead of under SU(3)F ⊗SU(2)S) then it is possible explain the mixing of pseudo scalar and vectorial mesons in the octet and singlet (η − η’ y ω − φ).​

Homework Equations

The Attempt at a Solution


I have no idea how to approach this problem.​
 
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  • #2
I tried to read some papers related to this topic, but I can't find any helpful resources. Any help would be greatly appreciated. Thanks in advance!
 

Related to Invariance of Hamiltonian of strong interaction under SU(6)

1. What is the Invariance of Hamiltonian of strong interaction under SU(6)?

The Invariance of Hamiltonian of strong interaction under SU(6) refers to the property of the Hamiltonian (a mathematical operator used to describe the total energy of a system) in quantum chromodynamics (QCD) being invariant under the special unitary group SU(6). This means that the Hamiltonian remains the same under certain transformations within this group, which is important in understanding the behavior of quarks and gluons in the strong nuclear force.

2. Why is the Invariance of Hamiltonian of strong interaction under SU(6) significant?

The Invariance of Hamiltonian of strong interaction under SU(6) is significant because it allows for the mathematical description of the strong nuclear force in terms of quarks and gluons. This invariance provides a framework for understanding the behavior and interactions of these fundamental particles, which are responsible for the stability of atomic nuclei.

3. How does the Invariance of Hamiltonian of strong interaction under SU(6) relate to the Standard Model of particle physics?

The Invariance of Hamiltonian of strong interaction under SU(6) is a key aspect of the Standard Model of particle physics. It is one of the fundamental symmetries of the strong nuclear force, which is a crucial component of the Standard Model. This symmetry allows for the prediction and understanding of the behavior of quarks and gluons, which are the building blocks of protons and neutrons.

4. Are there any experimental confirmations of the Invariance of Hamiltonian of strong interaction under SU(6)?

Yes, there have been several experimental confirmations of the Invariance of Hamiltonian of strong interaction under SU(6). One example is the measurement of the magnetic moments of baryons (particles made of three quarks) in the 1960s, which provided evidence for the existence of SU(6) symmetry. More recently, experiments at the Large Hadron Collider have also confirmed the predictions of SU(6) symmetry in the behavior of quarks and gluons.

5. How does the Invariance of Hamiltonian of strong interaction under SU(6) contribute to our understanding of the strong nuclear force?

The Invariance of Hamiltonian of strong interaction under SU(6) is a fundamental principle that helps us understand the behavior of the strong nuclear force. It allows for the classification of hadrons (particles made of quarks) into different representations of SU(6) and provides a framework for understanding their interactions. This symmetry also helps us make predictions and calculations about the properties and behavior of hadrons, which are crucial for our understanding of the strong nuclear force.

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