Feynman rules for electroweak multiplets

In summary, the standard model Lagrangian contains the interaction term Lγμ(i∂μ - g/2 τ·Wμ - g'/2 Y Bμ)L + Rγμ(i∂μ - g'/2 Y Bμ)R, where L and R are left- and right-handed fermions and τ are the three Pauli matrices. For isospin n fermions, the three SU(2) matrices are given by τ±|n m> = √(n∓m)(n±m+1) |n m±1> and τ3|n m> = m |n m>.
  • #1
Rocky Raccoon
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Can someone refer me to Feynman rules for electroweak interactions in the general case of SU(2) multiplets of weak isospin n and weak hypercharge Y interacting with EW gauge bosons?

I can only find the standard rules for SU(2) doublet electron - neutrino.

Thanks!
 
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  • #2
The interaction term in the standard model Lagrangian is

Lγμ(i∂μ - g/2 τ·Wμ - g'/2 Y Bμ)L + Rγμ(i∂μ - g'/2 Y Bμ)R

where L and R are left- and right-handed fermions and τ are the three Pauli matrices. So all you would have to do for an isospin n fermion is to replace τ by the three SU(2) matrices for isospin n, which are given by

τ±|n m> = √(n∓m)(n±m+1) |n m±1>
τ3|n m> = m |n m>
 

1. What are Feynman rules for electroweak multiplets?

Feynman rules for electroweak multiplets are a set of mathematical rules developed by physicist Richard Feynman to describe the interactions between particles in the electroweak theory. These rules are used to calculate the probability of particle interactions in high-energy experiments.

2. How are Feynman rules for electroweak multiplets different from other Feynman rules?

Feynman rules for electroweak multiplets differ from other Feynman rules in that they specifically describe the interactions between particles in the electroweak theory, which combines the electromagnetic and weak nuclear forces. Other Feynman rules may be used to describe interactions in other theories, such as quantum chromodynamics.

3. What is the purpose of using Feynman rules for electroweak multiplets?

The purpose of using Feynman rules for electroweak multiplets is to make predictions about the behavior and interactions of particles in the electroweak theory. These predictions can then be tested and compared to experimental data, helping to verify the accuracy of the theory.

4. How are Feynman rules for electroweak multiplets derived?

Feynman rules for electroweak multiplets are derived from the Lagrangian density of the electroweak theory, which describes the mathematical equations governing the behavior of particles in this theory. From the Lagrangian, Feynman diagrams can be constructed, which are then used to determine the Feynman rules for specific particle interactions.

5. Are Feynman rules for electroweak multiplets applicable to all particle interactions?

No, Feynman rules for electroweak multiplets are only applicable to interactions between particles in the electroweak theory. Other Feynman rules may be used to describe interactions in other theories, such as the strong nuclear force or gravity.

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