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Grassmann Integral into Lagrange for scalar superfields

  1. Nov 6, 2015 #1
    I have a more philosophical question about the interpretation of a mathematical process.
    We have a chiral superscalarfield shown as partiell Grassmann Integral and transform it into a lagrange.


    where S and P are real components of a complex scalarfield and D and G are real componentfields of F.
    It is a supersymmetric Transformation and covariant. Every Lorentz transformation is supersymmetric and covariant. genius so far.
    In the Grassmann equation is not a kinetic term and is only build now with a kinetic term through the lagrangian supersymmetric transformation.
    So if we work with Grassmann only and only think in Grassmann mathematic, then we have a complete different view on the world. We have a masseless world. But if we try to make it matching and kommensurable for our QT World, then we have other properties as in origin.
    We can interpretate it as SUSY or we can say that it is now the nature of the mathematic.

    What are you interpreting in this mathematical trick? It is more a philosophical question.
    Last edited: Nov 6, 2015
  2. jcsd
  3. Nov 6, 2015 #2
  4. Nov 7, 2015 #3


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    I am not sure whether you are just asking about the philosophical interpretation of superspace or supersymmetry itself. I don't think that one should try to interpret the Grassmann directions of superspace as being on the same physical footing as the spacetime coordinates. I would interpret superspace as a nice structure to use to construct supersymmetric theories.

    I would also add that it is possible to generate masses in the superspace formalism through a superpotential ##W(\Phi)##. The corresponding Lagrangian is the real part of ##\int d^2\theta W(\Phi)##.
  5. Nov 8, 2015 #4
    There's the rub. Grassmann Geometry is concret. For QT people it is only a nice instrument to establish Supersymmetry for their "Downgrade" into Lagrange.
  6. Nov 9, 2015 #5


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    I don’t do philosophy, and I’m not sure I understand your question. However, it is well known that super Lie groups play the same role on super spacetime which ordinary Lie groups play on ordinary spacetime. So, if supersymmetry is confirmed by experiments, one has to accept that the geometry of our spacetime is determined by the behaviour of geometrical object in superspace.
  7. Nov 9, 2015 #6
    IF supersymmetry is confirmed by experiments, then OK. But it doesn't seem so. (We should have found long before a Top sQuark, if SUSY is correct) What then?

    By the way I thought so, that you both argue from complete different views on this. One is arguing from the QT side and the other is argueing from the geometric side, which he hopes to find as reality.

    So if SUSY is not confirmed and will never be confirmed. What will you interpret in this kind of mathematical process? Will you go the way like Einstein was going with Tensorproducts and say that one result is imaginary and the other is correct for reality?

    Do we need lagrangian language in future for Descriptions of the whole bunch of the universe?
    Last edited: Nov 9, 2015
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