  We introduce a two-dimensional, distribution-valued field which we call the
quadratic field associated to the one-dimensional Ornstein-Uhlenbeck process.
We show that the stationary quadratic fluctuations of the simple exclusion
process, when rescaled in the diffusive scaling, converge to this quadratic
field. We show that this quadratic field evaluated at the diagonal corresponds
to the Wick-renormalized square of the Ornstein-Uhlenbeck process, and we use
this new representation in order to prove some small and large-time properties
of it.
