Why in SUSY we tend to use 2- components

In summary, the use of 2-component Weyl spinor fields in SUSY is preferred over ordinary Dirac fields because it aligns with the transformation from 2-complex components scalar fields and allows for dealing with left and right handed spinors separately. This also maintains the same number of degrees of freedom.
  • #1
Safinaz
259
8
Hi all,

why in SUSY we tend to use 2- components Weyl spinor field
not the ordinary Dirac filed ..

Regards,
Safinaz
 
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  • #2
It's also easier to work in the Standard Model using Weyl spinors instead of Dirac spinors. That's because the left handed Weyl spinors and the right handed Weyl spinors belong to two different representations of the electroweak gauge group. It makes more sense to deal with them separately.
 
  • #3
Is that also to match the transformation from 2- complex components scalar filed (4-degrees of freedom)
to 2- components Weyl spinor filed which are also complex so we have 4-degrees of freedom as well, instead
of Dirac filed which will be twice ..
 
  • #4
Yes, one Dirac field with four degrees of freedom corresponds to two Weyl fields with two degrees each.
 
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1. Why do we use 2-component SUSY instead of 4-component?

The use of 2-component SUSY is more convenient and mathematically elegant because it allows for the simplification of equations and calculations. It also provides a better description of the physical states in the theory.

2. How does 2-component SUSY handle spinor representations?

In 4-component SUSY, the spinor representations are complex, making the symmetry more difficult to work with. However, in 2-component SUSY, the spinor representations are real, simplifying the calculations and making the symmetry easier to manipulate.

3. What is the relationship between 2-component SUSY and superfields?

2-component SUSY is closely related to superfields, which are mathematical objects that describe the different components of a supersymmetric theory. The use of 2-component SUSY allows for a more compact and efficient representation of these superfields.

4. Can 2-component SUSY be used in all supersymmetric theories?

No, 2-component SUSY is not applicable to all supersymmetric theories. It is mainly used in theories with extended supersymmetry, such as N=2 or N=4, where a higher number of components would lead to unnecessary complexity.

5. Are there any drawbacks to using 2-component SUSY?

One potential drawback to using 2-component SUSY is that it may not fully capture all the intricacies of the supersymmetric theory. Some calculations and predictions may require the use of 4-component SUSY for a more accurate representation. However, the use of 2-component SUSY is still a valuable and widely used tool in studying supersymmetric theories.

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