Why in SUSY we tend to use 2- components

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Discussion Overview

The discussion centers on the preference for using 2-component Weyl spinor fields in supersymmetry (SUSY) rather than ordinary Dirac fields. It explores theoretical implications and representations within the context of the Standard Model.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants suggest that Weyl spinors are easier to work with in the Standard Model due to their representation under the electroweak gauge group, allowing for separate treatment of left-handed and right-handed components.
  • There is a proposal that the transformation from 2-component complex scalar fields to 2-component Weyl spinors maintains the same degrees of freedom, which is seen as advantageous compared to Dirac fields that have double the degrees of freedom.
  • One participant confirms that a single Dirac field with four degrees of freedom corresponds to two Weyl fields, each with two degrees of freedom.

Areas of Agreement / Disagreement

Participants generally agree on the advantages of using Weyl spinors in SUSY, particularly regarding degrees of freedom and representation in the Standard Model, but the discussion does not resolve all nuances or implications of these choices.

Contextual Notes

The discussion does not address potential limitations or assumptions regarding the transformation properties or the implications of using different spinor types in various theoretical frameworks.

Safinaz
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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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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.
 
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 ..
 
Yes, one Dirac field with four degrees of freedom corresponds to two Weyl fields with two degrees each.
 
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