Grassmann fields according to Peskin and Schroeder On page 301 in Peskin and Schroeder, they claim that a Grassman field $\psi(x)$ may be decomposed as 
$$\psi(x) = \sum_i c_i \phi_i(x),$$
where the $c_i$ are Grassmann numbers and the $\phi_i$ are "orthonormal basis functions".
I don't understand what is meant by "orthonormal basis function". Surely they would need to define some metric on the space of all fields to do this? I can't think of a natural one. 
They claim that for the Dirac field the $\phi_i$ are a basis of four component spinors. Presumably they mean spinor fields here. I don't know of a natural basis for these fields.
Could someone clear up whether this is an error in the book or whether I'm missing something?
 A: Even forgetting about the field for a second (meaning, forgetting about spatial-dependence and just focussing on one Grassmann number), a Grassmann number can be written as a linear combination of other Grassmann numbers, where the coefficients are complex numbers. For example P&S do that on the previous page (pg. 300) when they write a 'complex Grassmann number': $\theta = \frac{1}{\sqrt{2}}(\theta_1 +i\theta_2)$. Those numbers, $\theta_1$ and $\theta_2$, are independent Grassmann numbers, and we've expressed $\theta$ as a combination of them.
So what we're saying with the field is that, at some point in space $x$, there's a Grassmann number defined, which is equal to the linear combination $\sum_i\psi_i\phi_i(x)$. We allow for the fact that the Grassmann number at, say, $x_1$ is different from $x_2$ by allowing that the coefficients in the linear combinations of those two Grassman numbers will be different ($\phi_i(x_1)$ versus $\phi_i(x_2)$).
The orthonormal basis functions $\phi_i(x)$ are the usual orthonormal basis functions you're used to (sines, cosines, spherical harmonics, etc.).
All they're saying is that we have maximal freedom to allow the Grassmann number at $x_1$ to be whatever we want it to be regardless of what the number at $x_2$ is. Just like we can create any real-valued function we want by choosing the real-valued coefficients correctly in, say, a Fourier sum, we can create any Grassmann-valued function we want by correctly choosing the Grassmann-valued coefficients ($\psi_i$) in the sum you asked about.
