# Do the Grassmann coordinates in the superfield formalism have any physical meaning?

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?

• 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 – Avrham Aton Jun 2 '15 at 16:54
• @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? – Yossarian Jun 3 '15 at 13:57
• 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. – Avrham Aton Jun 3 '15 at 18:26

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.