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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?

Qmechanic
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Yossarian
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2 Answers2

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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.

Community
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Qmechanic
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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?

Michael C Price
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