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In the superfield formalism we consider fields in a space who has four so called bosonic coordinates $x^{\nu}$ and four so called fermionic coordinates $\theta_1$,$\theta_2$,$\bar{\theta_1}$,$\bar{\theta_2}$.

$x^{\mu}$ are of course the physical space-time coordinates, but, do the Grassmannian coordinates have an analog interpretation like some kind of extra dimension or should I view them as a mere formal artifact?

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  • $\begingroup$ This is why it's considered one of the most abstract contructs in physics, Most of it is just formalism - as the case is with the Grassmann coordinates $\endgroup$ – Avrham Aton Jun 2 '15 at 16:54
  • $\begingroup$ @AvrhamAton what about in supersymmetric theories with extra dimensions, like 11 dimensional supergravity? don't the extra dimensions have anything to do with the fermionic coordinates? $\endgroup$ – Yossarian Jun 3 '15 at 13:57
  • $\begingroup$ I think the difference is the following :whereas for instance in string theory the extra dimensions are an outcome of the theory, In the superfluid formalism they are part if the construct - a way to formulate the theory in a mathematically coherent way. Similarly the wave function in QM has no physical meaning as it is part of the construct of the theory. $\endgroup$ – Avrham Aton Jun 3 '15 at 18:26
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No measuring device in an experiment is going to measure a Grassmann-odd number, if that's what OP means by a physical meaning. A measuring device can only produce real outputs $\subseteq\mathbb{R}$. See also e.g. this Phys.SE post.

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The Grassmann numbers or coordinates are as real as complex numbers. You can do away with both, but that makes the equations more complicated and numerous. So, for simplicity, we use them. Yes, a measuring device can only measure real numbers - but what is a complex number other than just two real numbers, and a superfield a collection of 32 real numbers?

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