Transformation of auxiliary field

In summary, the transformation of auxiliary field is a useful tool in simplifying mathematical expressions in physical theories such as supersymmetry and gauge theories. In supersymmetry, the auxiliary field is transformed into a spinor field to cancel unphysical degrees of freedom, while in gauge theories it is transformed into a gauge field to mediate interactions between particles. This transformation can also lead to a more elegant form of equations of motion and reveal hidden symmetries and relationships. However, there are limitations to transforming auxiliary field and it is important to carefully consider its implications in a given theory.
  • #1
rbwang1225
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In West's book "Introduction to Strings and Branes", page 2, I don't understand why the auxiliary field e transformed as e'([itex]\tau'[/itex])d[itex]\tau'[/itex]=e([itex]\tau[/itex])d[itex]\tau[/itex].
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  • #2
By construction :-)

You impose several conditions on your action and then get how auxilary fields should transform. Just like with YM gauge field, you want gauge invarianceand from this you get transformation law
 

FAQ: Transformation of auxiliary field

1. What is the purpose of transforming auxiliary field?

The transformation of auxiliary field is used to simplify the mathematical expressions in certain physical theories, such as supersymmetry and gauge theories.

2. How is auxiliary field transformed in supersymmetry?

In supersymmetry, the auxiliary field is transformed into a spinor field, which is a fundamental component of the supersymmetry algebra. This transformation allows for the cancellation of unphysical degrees of freedom in the theory.

3. What is the role of auxiliary field in gauge theories?

In gauge theories, the auxiliary field is transformed into a gauge field, which mediates the interactions between particles. This allows for the theory to be invariant under local gauge transformations.

4. How does the transformation of auxiliary field affect the equations of motion in a theory?

The transformation of auxiliary field can lead to a simpler and more elegant form of the equations of motion in a theory. It can also help to reveal hidden symmetries and relationships between different physical quantities.

5. Are there any limitations to transforming auxiliary field?

Yes, there are limitations to transforming auxiliary field. It may not be possible in all theories, and even when it is possible, the transformed theory may not always be physically meaningful. It is important to carefully consider the implications and consequences of such transformations in a given theory.

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